Linear Regression TaskInstructions for Excel Practical: First attempt the linear regression task. Please use the data that is on the following slide, titled "Assignment Data" to complete the first...

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Linear Regression Task Instructions for Excel Practical: First attempt the linear regression task. Please use the data that is on the following slide, titled "Assignment Data" to complete the first part of the assignment. Then follow up with the next two tabs to perform a multiple regression using Excel. The first multiple regression example is already completed for you in the Lecture. Part 1: Complete the following Task Create a scatterplot of the data on the next tab. Be sure to label the axes and include a regression line. Be sure to include the equation and r-squared value and place it on the top right of the graph. Part 2: Interpret your results: please type in your answers to the following questions. Be sure to fully elaborate on them and try to include at least 2-3 sentences to explain each part. A. What kind of correlation (positive, negative, or no correlation) exists between the MPG of a car and its acceleration time? Is it a strong correlation? B. What are the degrees of freedom of the data set? Using the critical values table in the Lecture, is the R-squared Statistic significant enough for us to make any statistical inferences? If not, how large should the sample be to substantiate the results of this study? C. Should we interpret the y-intercept in this case? Why or why not? D. Using your equation, predict the MPG of a car that accelerates in 7.5 seconds. E. In a few sentences, summarize the findings of this study? What effect does MPG consumption have on the acceleration time of a vehicle? Linear Regression Data AccelerationMPGData retrieved from: https://www.consumerreports.org/fuel-economy-efficiency/vehicle-fuel-economy-vs-performance/ Honda Accord Hybrid EX7.447 Toyota Camry Hybrid LE7.847 Chevrolet Malibu Hybrid841 Hyundai Sonata Hybrid SE8.239 Ford Fusion SE Hybrid8.339 Toyota Camry LE (4-cyl.)832 Nissan Altima 2.5 SV7.631 Honda Accord EX (1.5T)7.731 Chevrolet Malibu LT (1.5T)8.429 Kia Optima EX (4-cyl.)828 Hyundai Sonata SEL (4-cyl.)8.328 Volkswagen Passat SE (4-cyl.)8.628 https://www.consumerreports.org/cars/honda/accordhttps://www.consumerreports.org/cars/kia/optimahttps://www.consumerreports.org/cars/hyundai/sonatahttps://www.consumerreports.org/cars/volkswagen/passathttps://www.consumerreports.org/cars/toyota/camryhttps://www.consumerreports.org/cars/chevrolet/malibuhttps://www.consumerreports.org/cars/hyundai/sonatahttps://www.consumerreports.org/cars/ford/fusionhttps://www.consumerreports.org/cars/toyota/camryhttps://www.consumerreports.org/cars/nissan/altimahttps://www.consumerreports.org/cars/honda/accordhttps://www.consumerreports.org/cars/chevrolet/malibu Mult Regression_Height HeightMomheightDadheightOutlier?PredictionError 666671 646268 646570Five Number Summary for Height 696676Minimum: 6663701st quartile: 636168Median: 6864693rd quartile: 656266Maximum: 647073 657075Outlier Parameters 666370IQR: 686869Lower Limit 666077Upper Limit 606165# of outliers 605962 606263 646072 706274 646170 636170 616067 696568 636465 666666 656470 646268 666473 656167 636067 636474 656275 666470 676470 67.56969 626060 646374 636268 646269 635874 62.56571.5 656472 66.56374 69.56672 63.56067 696474 676372 676670 676966 676568 676371 636069 636167 606066 636875 65.56271 666372 686770 656267 6563.569 666770 626369 666568 676471 636170 666069 676271 616369 626068 63.56263 616265 646163 616569 616468 636172 626272 646474 646268 656673 646167 596064 656768 636568 64.56266.5 646371 706276 606165 696873 626368 656972 646266 646470 666170 636268 676869 606068 686772 677076 666071 676872 656470 616464 646372 686471 646371 65.56270 676670 676974 62.565.568 626165 625765 646263 666673 656467 676570 64.56670 706577 635662 656471 606469 696475 646367 626266 636265 646970 626268 726572 636069 676966 686467 727076 59.55965 657070 686070 615967 666469 62.56771.5 656270 656370 636165 706871 646467 636566 686972 63.56469 67.57072 666571 666372 616165 636572 616067 616062 666570 636163 666267 666268 686369 626268 666770 636269 666272 666569 696670 686573 646574 696774 656370 676469 666767 636270 616666 676472 676371 63.56571 606466 676568 615970 636564 626466 676671 606265 64.565.566 60.56267 69.56374 666474 656267 636072 686674 686271 656371 636568 626067 636668 716972 636368 636366 626466 636167 656768 656473 645872 686872 646368 616267 626066 666271 686672 656468 696575 656972 646872 646470 676271 686567 736876 Attribution: n=214 female students at University of California at Davis Please perform the multiple regression for each of these tabs and do not delete them. Please include the output of your regressions to this assignment. Mult Regression_Bodyfat TricepsThighMidarmBodyfatz-scoreoutlier? 19.543.129.111.9 24.749.828.222.8 30.751.93718.7 29.854.331.120.1Outlier ParametersCalculate for Bodyfat Column 19.142.230.912.9IQR:mean: 25.653.923.721.7Lower Limitmedian: 31.458.527.627.1Upper Limitmode: 27.952.130.625.4# of outliersstandard deviation: 22.149.923.221.3# of outliers 25.553.524.819.3 31.156.63025.4 30.456.728.327.2 18.746.52311.7 19.744.228.617.8 14.642.721.312.8 29.554.430.123.9 27.755.325.722.6 30.258.624.625.4 22.748.227.114.8 25.25127.521.1 Attribution: Data source: Applied Regression Models, (4th edition), Kutner, Neter, and Nachtsheim Run a multiple regression that predicts bodyfat based on midarm, thigh, and triceps measurements. Write your equation here: Using the model, provided, find the predicted body fat of someone who has a triceps measurement of 21.4, thigh of 45.6, and midarm measurement of 27.6. Show your work below:
module-5-assignment-b41uqawu.xlsx
Answered Same DayOct 14, 2022

Answer To: Linear Regression TaskInstructions for Excel Practical: First attempt the linear regression task....

Rajeswari answered on Oct 15 2022
53 Votes
Sheet1
Sheet2
        Acceleration    MPG
    Honda Accord Hybrid EX    7.4    47
    Toyota Camry Hybrid LE    7.8    47                SUMMARY OUTPUT
    Chevrolet Malibu Hybrid    8    41                                            0.5423480262
    Hyundai Sonata Hybrid SE    8.2    39                Regression Statistics                            0.049304366
    Ford Fusion SE Hybrid    8.3    39                Multiple R    0.4767461579
    Toyota Camry LE (4-cyl.)    8    32                R Square    0.227286899
    Nissan Altima 2.5 SV    7.6    31                Adjusted R Square    0.150015589
    Honda Accord EX (1.5T)    7.7    31                Standard Error    6.6945768989
    Chevrolet Malibu LT (1.5T)    8.4    29                Observations    12
    Kia Optima EX (4-cyl.)    8    28
    Hyundai Sonata SEL (4-cyl.)    8.3    28                ANOVA
    Volkswagen Passat SE (4-cyl.)    8.6    28                    df    SS    MS    F    Significance F
                            Regression    1    131.8264014467    131.8264014467    2.9414138154    0.1171008772
                            Residual    10    448.1735985533    44.8173598553
                            Total    11    580
    a. POSITIVE correlation exists very weak.                             Coefficients    Standard Error    t Stat    P-value    Lower 95%    Upper 95%    Lower 95.0%    Upper 95.0%
    b.df = n-2    11    R^2 is not statistically significant.                Intercept    113.3634719711    45.7323712327    2.4788452668    0.0326072411    11.4653992712    215.2615446709    11.4653992712    215.2615446709
    test statistic =r/(1-r^2)^1/2 (n-2).        0.0493                Acceleration    -9.7649186257    5.6936473502    -1.7150550473    0.1171008772    -22.4511554418    2.9213181904    -22.4511554418    2.9213181904
    This lies below critical value for df 11.
    Critical value is 2.201.                            MPG = -9.76492*acceleration+113.3635
    c. y intercept is MPG when acceleration is 0.                                                                    R SQUARE     0.227
    we can interpret since acceleraton can be 0 as 113.3635 which is very high.                        RESIDUAL OUTPUT
    d.
    Substitute 7.5 seconds for accn in regression equation                        Observation    Predicted MPG    Residuals
    MPG for 7 accen    45.00906                    1    41.103074141    5.896925859
    e. MPG consumption does not have any significant                        2    37.1971066908    9.8028933092
    effect on time of aceleration.                        3    35.2441229656    5.7558770344
                            4    33.2911392405    5.7088607595
                            5    32.3146473779    6.6853526221
                            6    35.2441229656    -3.2441229656
                            7    39.1500904159    -8.1500904159
                            8    38.1735985533    -7.1735985533
                            9    31.3381555154    -2.3381555154
                            10    35.2441229656    -7.2441229656
                            11    32.3146473779    -4.3146473779
                            12    29.3851717902    -1.3851717902
Acceleration Line Fit Plot
MPG    7.4    7.8    8    8.1999999999999993    8.3000000000000007    8    7.6    7.7    8.4    8    8.3000000000000007    8.6    47    47    41    39    39    32    31    31    29    28    28    28    Predicted MPG    7.4    7.8    8    8.1999999999999993    8.3000000000000007    8    7.6    7.7    8.4    8    8.3000000000000007    8.6    41.103074141048822    37.197106690777574    35.244122965641949    33.291139240506332    32.314647377938506    35.244122965641949    39.150090415913198    38.173598553345386    31.338155515370698    35.244122965641949    32.314647377938506    29.385171790235081    Acceleration
MPG
MPG    7.4    7.8    8    8.1999999999999993    8.3000000000000007    8    7.6    7.7    8.4    8    8.3000000000000007    8.6    47    47    41    39    39    32    31    31    29    28    28    28    
Sheet3
    Height    Momheight    Dadheight    Outlier?    Prediction    Error
    66    66    71    no    64.9052    1.0948
    64    62    68    no    64.652    -0.652    SUMMARY OUTPUT
    64    65    70    no    65.7313    -1.7313
    69    66    76    no    67.1482    1.8518    Regression Statistics
    66    63    70    no    64.2138    1.7862    Multiple R    0.6584135618
    63    61    68    no    64.3485    -1.3485    R Square    0.4335084184
    68    64    69    no    64.1294    3.8706    Adjusted R Square    0.4281388299
    65    62    66    no    65.3937    -0.3937    Standard Error    2.0311519843
    64    70    73    no    68.109    -4.109    Observations    214
    65    70    75    no    66.7603    -1.7603
    66    63    70    no    66.3383    -0.3383    ANOVA
    68    68    69    no    63.5224    4.4776        df    SS    MS    F    Significance F
    66    60    77    no    66.9291    -0.9291    Regression    2    666.1489891845    333.0744945922    80.734011975    9.16030793474905E-27
    60    61    65    no    61.6673    -1.6673    Residual    211    870.4970388529    4.1255783832
    60    59    62    no    61.4141    -1.4141    Total    213    1536.6460280374
    60    62    63    no    61.195    -1.195
    64    60    72    no    65.2931    -1.2931        Coefficients    Standard Error    t Stat    P-value    Lower 95%    Upper 95%    Lower 95.0%    Upper 95.0%
    70    62    74    no    65.7654    4.2346    Intercept    18.5472520655    3.6927842427    5.02256586    0.0000010841    11.2677750647    25.8267290663    11.2677750647    25.8267290663
    64    61    70    no    64.2138    -0.2138    Momheight    0.3035055794    0.0544636172    5.5726298573    0.0000000761    0.1961430522    0.4108681067    0.1961430522    0.4108681067
    63    61    70    no    63.9103    -0.9103    Dadheight    0.3878555879    0.0472073211    8.2160050287    0    0.2947971837    0.4809139921    0.2947971837    0.4809139921
    61    60    67    no    64.2641    -3.2641
    69    65    68    no    64.3485    4.6515        ht = 0.3879*dad height + 0.3035*mom ht + 18.5473
    63    64    65    no    63.7918    -0.7918
    66    66    66    no    63.5727    2.4273    RESIDUAL OUTPUT
    65    64    70    no    64.5173    0.4827
    64    62    68    no    64.3485    -0.3485    Observation    Predicted Height    Residuals
    66    64    73    no    65.3775    0.6225    1    66.116367047    -0.116367047
    65    61    67    no    62.7466    2.2534    2    63.7387779657    0.2612220343
    63    60    67    no    63.9606    -0.9606    3    65.4250058797    -1.4250058797
    63    64    74    no    66.0689    -3.0689    4    68.0556449865    0.9443550135                    Five Number Summary for Height
    65    62    75    no    67.0638    -2.0638    5    64.8179947209    1.1820052791                    Minimum:        59
    66    64    70    no    65.1243    0.8757    6    63.4352723863    -0.4352723863                    1st quartile:        63
    67    64    70    no    66.6418    0.3582    7    64.7336447124    3.2663552876                    Median:        65
    67.5    69    69    no    63.5224    3.9776    8    62.9630667899    2.0369332101                    3rd quartile:        67
    62    60    60    no    60.9418    1.0582    9    68.1061005404    -4.1061005404                    Maximum:        73
    64    63    74    no    66.0689    -2.0689    10    68.8818117162    -3.8818117162
    63    62    68    no    63.7415    -0.7415    11    64.8179947209    1.1820052791                    Outlier Parameters
    64    62    69    no    62.9154    1.0846    12    65.94766703    2.05233297                    IQR:        4
    63    58    74    no    66.9794    -3.9794    13    66.6224670979    -0.6224670979                    Lower Limit        57
    62.5    65    71.5    no    65.70615    -3.20615    14    62.2717056226    -2.2717056226                    Upper Limit        73
    65    64    72    no    65.5966    -0.5966    15    60.5011277001    -0.5011277001                    # of...
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