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Q1 Visits During Office Hours During the Semester Grade None One or two Three or more Total C or worse5615244221507 B5404984901528 A4205015801501 Total1521152314924536 Visits During Office Hours During the Semester-- Percentaged Table Grade None One or two Three or more C or worse37%34%28% B36%33%33% A28%33%39% Total100%100%100% Red Light Cameras Group 1 - Control (No Camera)Group 2 - Experimental (Red Light Cameras) Accidents in Pretest yearAccidents in Test yearAccidents in Pretest yearAccidents in Test yearGroup 1 Control Accidents in Test YearGreoup 2 Experiment Accidents in Test Year 10765 20171817Mean:11.75Mean:14.525 25231912 24161611 21191615t-Test: Two-Sample Assuming Unequal Variances 191754 23211514Variable 1Variable 2 1113118Mean11.7514.525Difference between the menas2.775 16141616Variance35.525641025633.0762820513 23151814Observations4040 17201614Hypothesized Mean Difference0 24232626df78 651515t Stat-2.1189701461 981918P(T<=t) one-tail="" 0.0186376134="" 11="" 10="" 22="" 18="" t="" critical="" one-tail="" 1.6646246445="" 13="" 12="" 12="" 13=""><=t) two-tail0.0372752269 109127t critical two-tail1.9908470688 65910 5181112 11111011 1761615group 1grooup 2 5579sum621581 1111810 24131719 892729 451012 57810 25272219 16182321 8101010 8102726 1771211 6987 581918 14122417 1691918 561616 552016 661112 442526 food deserts distance (km)weight (kg) 0.7107.0 0.4136.1 1.9103.9 1.5111.6 0.2144.7 2.295.7 0.1144.7 0.5121.6 0.897.1 3.4131.1 1145.1 0.888.5 0.993.0 2.178.0 2.180.7 1.8105.2 1.7117.0 0.8103.4 1.1113.4 0.1108.4 2.199.8 3.779.4 1.8103.9 1.689.4 2.1113.9 3.480.7 2143.8 0.5129.7 0.1107.5 2.293.9 2101.6 1.9103.0 0.8115.7 1.6109.8 0.991.6 1.5112.0 1.7106.6 3.978.9 0.983.9 2.393.4 3.278.0 0.390.7 1.689.8 0.6118.4 0.3140.2 2.886.6 284.8 0.2113.4 0.8103.9 0.3137.0 1 you are a professor of statistics and you are curious to see the relationship between student office hour attendance and the final grade a student receives in a course. thankfully, you have a lot of data from a variety of programs that showed the following: visits during office hours during the semester grade none one or two three or more c or worse 561 524 422 b 540 498 490 a 420 501 580 you hypothesize that the more visits made to office hours, the higher the likely grade. now you must select the appropriate statistical test and evaluate the results to say whether there is a significant relationship between office hour visits and grade. as a part of your answer you must discuss all pertinent stats and provide/discuss a percentaged table. in doing so, make sure to address the differences in each category that you observe and what they mean. in order to get credit, you must: · state the null and alternative hypotheses · null hypothesis: there is no significant relationship between the number of visits made to officer hours and higher grades. · alternative hypothesis: there is a significant relationship between the number of visits made to office hours and a higher grade. · generate a percentaged table to show the magnitude of differences between categories · i will run a chi squared test and calculate gamma test to determine if there is a statistical significance and the strength between the two values. and why you selected that test · · using the online chi squared calculator, i found that the chi-square statistic is 48.86 and the p-value is 0.00001. since the p-value is below the alpha of .05, e can reject the null hypothesis and claim there is a significant relationship between the number of visits made to office hours and a higher grade in the class. · calculate gamma as a measure of strength and direction of association · · finally, construct a paragraph explaining your approach and findings to your supervisor that includes a brief discussion of all key statistics (chi square value, p value, gamma), the results of your hypothesis test, as well as the percentaged table you constructed. 2 the tucson, arizona city council was approached several years ago by a firm that wanted to lease the city red light cameras to install in intersections. in exchange for a portion of all of the fines collected from red light violations, the firms would set up cameras that would take a photo of the license plate of any car that entered into the intersection after the light had turned red. the city then could mail out a citation to the offender. the goal of the program was to not only yield some added revenue for the city but also to reduce the number of accidents due to cars speeding through red lights. the city council, nevertheless, was a bit wary of the vendor because they had heard that in other cities citizens were displeased with the program. moreover, their analysts had found evidence that red light cameras may actually increase the number of accidents because drivers end up slamming on the brakes when the yellow light comes on leading to a rear end accident if the car behind them was caught by surprise. consequently, the city council astutely decided to conduct a preliminary experiment before agreeing to a contract with the red light camera vendor. it identified 80 intersections controlled by red-lights that also experienced a heavy amount of traffic. these intersections were a mix of intersections in the heavily travelled downtown core of the city as well as other intersections in the outskirts of the city. it had its staff randomly place each intersection into one of two treatment groups: · group 1 40 intersections were left as they were to act as the control group. · group 2 40 intersections had red light cameras installed. the data collected in these experiments are provided in the excel spreadsheet. the variables are: experimental condition: group 1 (control) – no cameras; group 2 ( experimental) – cameras accident in pretest year: total number of accidents recorded in the intersection in the year prior to the beginning of the experiment accident in test year: total number of accidents recorded in the intersection in the year during the experiment your assignment is to analyze these data for the city council to see whether the red light cameras seem to affect the number of accidents. · calculate the average number of accidents for the control group and experimental group of intersections in the test year. (post-test only comparison). what do you observe? · the average number of accidents in the experimental group (14.525) is higher than that of the control group (11.75). · you want to be sure that your conclusion is statistically valid. so, you will need to conduct a hypothesis test comparing each group (experimental and control) using the test year data only. state the null and alternative hypotheses for this test. · null hypothesis: the red-light cameras do not have an effect on the number of accidents. · alternative hypothesis: the red-light cameras have an effect on the numebr of accidents. · conduct a “one tailed t-test: two samples assuming unequal variance” using excel, an online statistics calculator or by hand. are you able to reject the null hypothesis, again, just looking at the test year results? in responding to this, reference the p value associated with your t score, state alpha, and interpret your hypotheses based on your results. · the one-tailed t-test assuming unequal variances identified the p-value as 0.019 and the t – score as 1.67. with the alpha based at 0.5 (maybe? or 0.05, sometimes it’s the other) we can reject the null hypothesis and state red light cameras have an effect on the number of accidents. · as an analyst, you aren’t so sure this was the best way to go about things, so you decide to calculate the difference between the pre-test number of accidents and the test-year number of accidents for each intersection. what is the average change in the number of accidents for the control (group 1) versus the experimental group (group 2)? · the pre-test number of accidents is 621 and posttest is 581, with on average of 11.75 and 14.525 respectfully. the average change between the two is 2.775. · conduct another hypothesis test to check whether this difference is statistically significant between the control and experimental groups. again, state your null and alternative hypothesis, conduct the same type of t-test, and interpret your results. · do the results of your hypothesis tests in parts #3 and #5 agree? explain why they do or do not lead to the same conclusion. based on what we learned at the beginning of the semester regarding study validity, which of the two tests is giving the most useful results? why do you think that? 3 you are conducting research on the impact of food deserts on community health. in doing so, you are looking into variables that may contribute to obesity. some early research has pointed to the relationship of the distance of an individual’s home from a convenience store and obesity (convenience stores are not known for their healthy food options). you decide it is important to explore this idea further, and collect data from a sample of 50 male participants in the community. the data you collect include distance of each participant’s home from a convenience store (in kilometers) and the client’s weight (in kilograms). the data are included in the attached spreadsheet. you contend that as distance to a convenience store decreases, weight increases. in order to evaluate this contention, do the following: · clearly identify the dependent variable and independent variable, and support your decision · food deserts are the independent variable and community health is the dependent variable. · or the distance of an individual's home is the independent variable and obesity is the dependent variable · in both cases, we’re stating that the dependent variable can be altered by the independent. · graph the relationship between the variables in excel (or equivalent) and include the best fit line, the regression equation and the coefficient of determination – make sure to include the dv and iv on the correct axes. please remember our standard rules for creating graphics, including labeling axes, providing units, providing a clear title, etc. · provide a brief summary of your findings, making sure to discuss the slope (what it is and what it means in relation to your variables), the intercept (again, what it is and what it means in relation to your variables), and the coefficient of determination (what it tells you about your regression model). in doing so, make sure to explain in clear terms what your model shows, whether or not you think this is an important finding, and also identify other variables you might consider including in your study as contributors to obesity in future investigations. · finally, what weight does your model predict if a male lives 5 miles away from a convenience store? how about 10 miles? from the difference in these two answers, indicate what we have to be careful of when it comes to using regression models? 4 you are heading two-tail="" 0.0372752269="" 10="" 9="" 12="" 7="" t="" critical="" two-tail="" 1.9908470688="" 6="" 5="" 9="" 10="" 5="" 18="" 11="" 12="" 11="" 11="" 10="" 11="" 17="" 6="" 16="" 15="" group="" 1="" grooup="" 2="" 5="" 5="" 7="" 9="" sum="" 621="" 581="" 11="" 11="" 8="" 10="" 24="" 13="" 17="" 19="" 8="" 9="" 27="" 29="" 4="" 5="" 10="" 12="" 5="" 7="" 8="" 10="" 25="" 27="" 22="" 19="" 16="" 18="" 23="" 21="" 8="" 10="" 10="" 10="" 8="" 10="" 27="" 26="" 17="" 7="" 12="" 11="" 6="" 9="" 8="" 7="" 5="" 8="" 19="" 18="" 14="" 12="" 24="" 17="" 16="" 9="" 19="" 18="" 5="" 6="" 16="" 16="" 5="" 5="" 20="" 16="" 6="" 6="" 11="" 12="" 4="" 4="" 25="" 26="" food="" deserts="" distance="" (km)="" weight="" (kg)="" 0.7="" 107.0="" 0.4="" 136.1="" 1.9="" 103.9="" 1.5="" 111.6="" 0.2="" 144.7="" 2.2="" 95.7="" 0.1="" 144.7="" 0.5="" 121.6="" 0.8="" 97.1="" 3.4="" 131.1="" 1="" 145.1="" 0.8="" 88.5="" 0.9="" 93.0="" 2.1="" 78.0="" 2.1="" 80.7="" 1.8="" 105.2="" 1.7="" 117.0="" 0.8="" 103.4="" 1.1="" 113.4="" 0.1="" 108.4="" 2.1="" 99.8="" 3.7="" 79.4="" 1.8="" 103.9="" 1.6="" 89.4="" 2.1="" 113.9="" 3.4="" 80.7="" 2="" 143.8="" 0.5="" 129.7="" 0.1="" 107.5="" 2.2="" 93.9="" 2="" 101.6="" 1.9="" 103.0="" 0.8="" 115.7="" 1.6="" 109.8="" 0.9="" 91.6="" 1.5="" 112.0="" 1.7="" 106.6="" 3.9="" 78.9="" 0.9="" 83.9="" 2.3="" 93.4="" 3.2="" 78.0="" 0.3="" 90.7="" 1.6="" 89.8="" 0.6="" 118.4="" 0.3="" 140.2="" 2.8="" 86.6="" 2="" 84.8="" 0.2="" 113.4="" 0.8="" 103.9="" 0.3="" 137.0="" 1="" you="" are="" a="" professor="" of="" statistics="" and="" you="" are="" curious="" to="" see="" the="" relationship="" between="" student="" office="" hour="" attendance="" and="" the="" final="" grade="" a="" student="" receives="" in="" a="" course. ="" thankfully,="" you="" have="" a="" lot="" of="" data="" from="" a="" variety="" of="" programs="" that="" showed="" the="" following:="" ="" ="" visits="" during="" office="" hours="" during="" the="" semester="" grade="" none="" one="" or="" two="" three="" or="" more="" c="" or="" worse="" 561="" 524="" 422="" b="" 540="" 498="" 490="" a="" 420="" 501="" 580="" ="" you="" hypothesize="" that="" the="" more="" visits="" made="" to="" office="" hours,="" the="" higher="" the="" likely="" grade. ="" now="" you="" must="" select="" the="" appropriate="" statistical="" test="" and="" evaluate="" the="" results="" to="" say="" whether="" there="" is="" a significant="" relationship between="" office="" hour="" visits="" and="" grade.="" as="" a="" part="" of="" your="" answer="" you="" must="" discuss="" all="" pertinent="" stats="" and="" provide/discuss="" a percentaged table. ="" in="" doing="" so,="" make="" sure="" to="" address="" the="" differences="" in="" each="" category="" that="" you="" observe="" and="" what="" they="" mean. ="" in="" order="" to="" get="" credit,="" you="" must:="" ="" ·="" state="" the="" null="" and="" alternative="" hypotheses="" ·="" null="" hypothesis:="" there="" is="" no="" significant="" relationship="" between="" the="" number="" of="" visits="" made="" to="" officer="" hours="" and="" higher="" grades.="" ·="" alternative="" hypothesis:="" there="" is="" a="" significant="" relationship="" between="" the="" number="" of="" visits="" made="" to="" office="" hours="" and="" a="" higher="" grade.="" ·="" generate="" a="" percentaged="" table="" to="" show="" the="" magnitude="" of="" differences="" between="" categories="" ·="" i="" will="" run="" a="" chi="" squared="" test="" and="" calculate="" gamma="" test="" to="" determine="" if="" there="" is="" a="" statistical="" significance="" and="" the="" strength="" between="" the="" two="" values.="" and="" why="" you="" selected="" that="" test="" ·="" ·="" using="" the="" online="" chi="" squared="" calculator,="" i="" found="" that="" the="" chi-square="" statistic="" is="" 48.86="" and="" the="" p-value="" is="" 0.00001.="" since="" the="" p-value="" is="" below="" the="" alpha="" of="" .05,="" e="" can="" reject="" the="" null="" hypothesis="" and="" claim="" there="" is="" a="" significant="" relationship="" between="" the="" number="" of="" visits="" made="" to="" office="" hours="" and="" a="" higher="" grade="" in="" the="" class.="" ·="" calculate="" gamma="" as="" a="" measure="" of="" strength="" and="" direction="" of="" association="" ·="" ·="" finally,="" construct="" a="" paragraph="" explaining="" your="" approach="" and="" findings="" to="" your="" supervisor="" that="" includes="" a="" brief="" discussion="" of="" all="" key="" statistics="" (chi="" square="" value,="" p="" value,="" gamma),="" the="" results="" of="" your="" hypothesis="" test,="" as="" well="" as="" the="" percentaged="" table="" you="" constructed.="" 2="" the="" tucson,="" arizona="" city="" council="" was="" approached="" several="" years="" ago="" by="" a="" firm="" that="" wanted="" to="" lease="" the="" city="" red="" light="" cameras="" to="" install="" in="" intersections. ="" in="" exchange="" for="" a="" portion="" of="" all="" of="" the="" fines="" collected="" from="" red="" light="" violations,="" the="" firms="" would="" set="" up="" cameras="" that="" would="" take="" a="" photo="" of="" the="" license="" plate="" of="" any="" car="" that="" entered="" into="" the="" intersection="" after="" the="" light="" had="" turned="" red. ="" the="" city="" then="" could="" mail="" out="" a="" citation="" to="" the="" offender. ="" the="" goal="" of="" the="" program="" was="" to="" not="" only="" yield="" some="" added="" revenue="" for="" the="" city="" but="" also="" to="" reduce="" the="" number="" of="" accidents="" due="" to="" cars="" speeding="" through="" red="" lights.="" ="" the="" city="" council,="" nevertheless,="" was="" a="" bit="" wary="" of="" the="" vendor="" because="" they="" had="" heard="" that="" in="" other="" cities="" citizens="" were="" displeased="" with="" the="" program. moreover,="" their="" analysts="" had="" found="" evidence="" that="" red="" light="" cameras="" may="" actually="" increase="" the="" number="" of="" accidents="" because="" drivers="" end="" up="" slamming="" on="" the="" brakes="" when="" the="" yellow="" light="" comes="" on="" leading="" to="" a="" rear="" end="" accident="" if="" the="" car="" behind="" them="" was="" caught="" by="" surprise. ="" ="" consequently,="" the="" city="" council="" astutely="" decided="" to="" conduct="" a="" preliminary="" experiment="" before="" agreeing="" to="" a="" contract="" with="" the="" red="" light="" camera="" vendor. ="" it="" identified="" 80="" intersections="" controlled="" by="" red-lights="" that="" also="" experienced="" a="" heavy="" amount="" of="" traffic. ="" these="" intersections="" were="" a="" mix="" of="" intersections="" in="" the="" heavily="" travelled="" downtown="" core="" of="" the="" city="" as="" well="" as="" other="" intersections="" in="" the="" outskirts="" of="" the="" city. ="" it="" had="" its="" staff="" randomly="" place="" each="" intersection="" into="" one="" of="" two="" treatment="" groups:="" ="" ·="" group="" 1 ="" 40="" intersections="" were="" left="" as="" they="" were="" to="" act="" as="" the="" control="" group. ="" ·="" group="" 2 40="" intersections="" had="" red="" light="" cameras="" installed.="" ="" the="" data="" collected="" in="" these="" experiments="" are="" provided="" in="" the="" excel="" spreadsheet. ="" the="" variables="" are:="" experimental="" condition: group 1="" (control)="" –="" no="" cameras; ="" group="" 2="" (="" experimental)="" –="" cameras="" accident="" in="" pretest="" year: total number="" of="" accidents="" recorded="" in="" the="" intersection="" in="" the="" year="" prior="" to="" the="" beginning="" of="" the="" experiment="" accident="" in="" test="" year: ="" total number="" of="" accidents="" recorded="" in="" the="" intersection="" in="" the="" year="" during="" the="" experiment="" ="" your="" assignment="" is="" to="" analyze="" these="" data="" for="" the="" city="" council="" to="" see="" whether="" the="" red="" light="" cameras="" seem="" to="" affect="" the="" number="" of="" accidents.="" ="" ·="" calculate="" the="" average="" number="" of="" accidents="" for="" the="" control="" group="" and="" experimental="" group="" of="" intersections in="" the="" test="" year. ="" (post-test="" only="" comparison). ="" what="" do="" you="" observe?="" ·="" the="" average="" number="" of="" accidents="" in="" the="" experimental="" group="" (14.525)="" is="" higher="" than="" that="" of="" the="" control="" group="" (11.75).="" ·="" you="" want="" to="" be="" sure="" that="" your="" conclusion="" is="" statistically="" valid. ="" so,="" you="" will="" need="" to="" conduct="" a="" hypothesis="" test="" comparing="" each="" group="" (experimental="" and="" control)="" using="" the="" test="" year="" data="" only. ="" state="" the="" null="" and="" alternative="" hypotheses="" for="" this="" test. ="" ·="" null="" hypothesis:="" the="" red-light="" cameras="" do="" not="" have="" an="" effect="" on="" the="" number="" of="" accidents.="" ·="" alternative="" hypothesis:="" the="" red-light="" cameras="" have="" an="" effect="" on="" the="" numebr="" of="" accidents.="" ·="" conduct="" a="" “one="" tailed="" t-test: ="" two="" samples="" assuming="" unequal="" variance”="" using="" excel,="" an="" online="" statistics="" calculator="" or="" by="" hand. ="" are="" you="" able="" to="" reject="" the="" null="" hypothesis,="" again, just="" looking="" at="" the="" test="" year="" results?="" in="" responding="" to="" this,="" reference="" the="" p="" value="" associated="" with="" your="" t="" score,="" state="" alpha,="" and="" interpret="" your="" hypotheses="" based="" on="" your="" results.="" ·="" the="" one-tailed="" t-test="" assuming="" unequal="" variances="" identified="" the="" p-value="" as="" 0.019="" and="" the="" t="" –="" score="" as="" 1.67.="" with="" the="" alpha="" based="" at="" 0.5="" (maybe?="" or="" 0.05,="" sometimes="" it’s="" the="" other)="" we="" can="" reject="" the="" null="" hypothesis="" and="" state="" red="" light="" cameras="" have="" an="" effect="" on="" the="" number="" of="" accidents.="" ·="" as="" an="" analyst,="" you="" aren’t="" so="" sure="" this="" was="" the="" best="" way="" to="" go="" about="" things,="" so="" you="" decide="" to="" calculate="" the difference="" between="" the="" pre-test="" number="" of="" accidents="" and="" the="" test-year="" number="" of="" accidents="" for="" each="" intersection. ="" what="" is="" the="" average change in="" the="" number="" of="" accidents="" for="" the="" control="" (group="" 1)="" versus="" the="" experimental="" group="" (group="" 2)?="" ·="" the="" pre-test="" number="" of="" accidents="" is="" 621="" and="" posttest="" is="" 581,="" with="" on="" average="" of="" 11.75="" and="" 14.525="" respectfully.="" the="" average="" change="" between="" the="" two="" is="" 2.775.="" ·="" conduct="" another="" hypothesis="" test="" to="" check="" whether this difference="" is="" statistically="" significant="" between="" the="" control="" and="" experimental="" groups. ="" again,="" state="" your="" null="" and="" alternative="" hypothesis,="" conduct="" the="" same="" type="" of="" t-test,="" and="" interpret="" your="" results.="" ·="" do="" the="" results="" of="" your="" hypothesis="" tests="" in="" parts="" #3="" and="" #5="" agree? ="" explain="" why="" they="" do="" or="" do="" not="" lead="" to="" the="" same="" conclusion. ="" based="" on="" what="" we="" learned="" at="" the="" beginning="" of="" the="" semester="" regarding="" study="" validity,="" which="" of="" the="" two="" tests="" is="" giving="" the="" most="" useful="" results? ="" why="" do="" you="" think="" that? ="" 3="" you="" are="" conducting="" research="" on="" the="" impact="" of="" food="" deserts="" on="" community="" health. ="" in="" doing="" so,="" you="" are="" looking="" into="" variables="" that="" may="" contribute="" to="" obesity. ="" some="" early="" research="" has="" pointed="" to="" the="" relationship="" of="" the="" distance="" of="" an="" individual’s="" home="" from="" a="" convenience="" store="" and="" obesity="" (convenience="" stores="" are="" not="" known="" for="" their="" healthy="" food="" options). ="" you="" decide="" it="" is="" important="" to="" explore="" this="" idea="" further,="" and="" collect="" data="" from="" a="" sample="" of="" 50="" male="" participants="" in="" the="" community.="" the="" data="" you="" collect="" include="" distance="" of="" each="" participant’s="" home="" from="" a="" convenience="" store="" (in="" kilometers)="" and="" the="" client’s="" weight="" (in="" kilograms).="" the="" data="" are="" included="" in="" the="" attached="" spreadsheet. ="" you="" contend="" that="" as="" distance="" to="" a="" convenience="" store="" decreases,="" weight="" increases.="" in="" order="" to="" evaluate="" this="" contention,="" do="" the="" following:="" ="" ·="" clearly="" identify="" the="" dependent="" variable="" and="" independent="" variable,="" and="" support="" your="" decision="" ·="" food="" deserts="" are="" the="" independent="" variable="" and="" community="" health="" is="" the="" dependent="" variable.="" ·="" or="" the="" distance="" of="" an="" individual's="" home="" is="" the="" independent="" variable="" and="" obesity="" is="" the="" dependent="" variable="" ·="" in="" both="" cases,="" we’re="" stating="" that="" the="" dependent="" variable="" can="" be="" altered="" by="" the="" independent.="" ·="" graph="" the="" relationship="" between="" the="" variables="" in="" excel="" (or="" equivalent)="" and="" include="" the="" best="" fit="" line,="" the="" regression="" equation="" and="" the="" coefficient="" of="" determination="" –="" make="" sure="" to="" include="" the="" dv="" and="" iv="" on="" the="" correct="" axes. ="" please="" remember="" our="" standard="" rules="" for="" creating="" graphics,="" including="" labeling="" axes,="" providing="" units,="" providing="" a="" clear="" title,="" etc.="" ·="" provide="" a="" brief="" summary="" of="" your="" findings,="" making="" sure="" to="" discuss="" the="" slope="" (what="" it="" is="" and="" what="" it="" means="" in="" relation="" to="" your="" variables),="" the="" intercept="" (again,="" what="" it="" is="" and="" what="" it="" means="" in="" relation="" to="" your="" variables),="" and="" the="" coefficient="" of="" determination="" (what="" it="" tells="" you="" about="" your="" regression="" model). ="" in="" doing="" so,="" make="" sure="" to="" explain="" in="" clear="" terms="" what="" your="" model="" shows,="" whether="" or="" not="" you="" think="" this="" is="" an="" important="" finding,="" and="" also="" identify="" other="" variables="" you="" might="" consider="" including="" in="" your="" study="" as="" contributors="" to="" obesity="" in="" future="" investigations.="" ·="" finally,="" what="" weight="" does="" your="" model="" predict="" if="" a="" male="" lives="" 5="" miles="" away="" from="" a="" convenience="" store?="" how="" about="" 10="" miles? ="" from="" the="" difference="" in="" these="" two="" answers,="" indicate="" what="" we="" have="" to="" be="" careful="" of="" when="" it="" comes="" to="" using="" regression="" models?="" ="" 4="" you="" are="">