Please ensure the directions are specifically followed. Each problem requires the followingHypothesized Model: State your hypothesized model as ˆy = β0 +β1x with numerical values for β0 and β + 1 ˆ A...

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Please ensure the directions are specifically followed. Each problem requires the followingHypothesized Model: State your hypothesized model as ˆy = β0 +β1x with numerical values for β0 and β + 1 ˆ A scatterplot showing your hypothesized model overlaying the original data. ˆ Parameter estimates and confidence intervals where requested (unless otherwise noted, use the tdistribution for tests/intervals) ˆ A test for validity in your model (either slope or coefficient of correlation), remember all portions of a hypothesis test – Null and Alternative Hypothesis – Test Statistic – Either p-value or a critical value to compare – Correctly stated conclusion ˆ Predictions and estimates (where requested) for your model. ˆ Validation of your assumptions for Regression


as well as the other questions asked
Requesting a word document with all visuals in the word document (scatter plots, ect)


DASC 512, Homework 6 Instructions: Each problem will require you to perform a simple regression analysis. A regression analysis includes the following information/steps: ˆ Hypothesized Model: State your hypothesized model as ŷ = β0 +β1x with numerical values for β0 and β + 1 ˆ A scatterplot showing your hypothesized model overlaying the original data. ˆ Parameter estimates and confidence intervals where requested (unless otherwise noted, use the t- distribution for tests/intervals) ˆ A test for validity in your model (either slope or coefficient of correlation), remember all portions of a hypothesis test – Null and Alternative Hypothesis – Test Statistic – Either p-value or a critical value to compare – Correctly stated conclusion ˆ Predictions and estimates (where requested) for your model. ˆ Validation of your assumptions for Regression 1. In baseball, it is hypothesized that we can use the run differential to predict the number of wins a team will have by the end of the season. Use the file ‘TeamData.csv’ to test this concept. Note: The only thing different from HW5 is the graphical analysis of your assumptions. (a) Create a column of data for Run Differential (R−RA) and a column for Win Percentage (W/(W+ L)). Use these values to determine if the Run Differential can be used to predict the percentage of wins a team will end up with and graphically validate that your regression model (Residual Analysis) (b) Bill James, the godfather of sabermetrics, emperically derived a non-linear formula to estimate winning percentage called the Pythagorean Expectation. Wpct = R2 R2 +RA2 Create a new variable representing R 2 R2+RA2 , the pythagorean model. Now use this new column to replace the Run Differential and re-run your analysis, perform a graphical analysis on the residuals to validate this model. HW 6, DASC 512, Page 1 2. Using the data file ‘UScrime.csv’ fit a model that can be used to predict the rate of offenses per 1000000 population in 1960 (Achieve an R2a ≥ 0.7). Run residual analysis (graphically) to determine if your model is accurate. The data is aggregating data from 47 states in the US in 1960 with the following columns: Variable Description M percentage of males aged 14–24 in total state population So indicator variable for a southern state Ed mean years of schooling of the population aged 25 years or over Po1 per capita expenditure on police protection in 1960 Po2 per capita expenditure on police protection in 1959 LF labour force participation rate of civilian urban males in the age-group 14-24 M.F number of males per 100 females Pop state population in 1960 in hundred thousands NW percentage of nonwhites in the population U1 unemployment rate of urban males 14–24 U2 unemployment rate of urban males 35–39 Wealth wealth: median value of transferable assets or family income Ineq income inequality: percentage of families earning below half the median income Prob probability of imprisonment: ratio of number of commitments to number of offenses Time average time in months served by offenders in state prisons before their first release Crime crime rate: number of offenses per 100,000 population in 1960 Helpful hint: Only one of Po1 and Po2, and only one of U1 and U2, remain in the final regression, because of high collinearity. Once your model is complete, noting that this is not implying a causal relationship, comment on the level of association (slope) between the variables in your model with crime rates. What does a positive/negative slope mean? HW 6, DASC 512, Page 2 "","M","So","Ed","Po1","Po2","LF","M.F","Pop","NW","U1","U2","Wealth","Ineq","Prob","Time","Crime" "1",15.1,1,9.1,5.8,5.6,0.51,95,33,30.1,0.108,4.1,3940,26.1,0.084602,26.2011,791 "2",14.3,0,11.3,10.3,9.5,0.583,101.2,13,10.2,0.096,3.6,5570,19.4,0.029599,25.2999,1635 "3",14.2,1,8.9,4.5,4.4,0.533,96.9,18,21.9,0.094,3.3,3180,25,0.083401,24.3006,578 "4",13.6,0,12.1,14.9,14.1,0.577,99.4,157,8,0.102,3.9,6730,16.7,0.015801,29.9012,1969 "5",14.1,0,12.1,10.9,10.1,0.591,98.5,18,3,0.091,2,5780,17.4,0.041399,21.2998,1234 "6",12.1,0,11,11.8,11.5,0.547,96.4,25,4.4,0.084,2.9,6890,12.6,0.034201,20.9995,682 "7",12.7,1,11.1,8.2,7.9,0.519,98.2,4,13.9,0.097,3.8,6200,16.8,0.0421,20.6993,963 "8",13.1,1,10.9,11.5,10.9,0.542,96.9,50,17.9,0.079,3.5,4720,20.6,0.040099,24.5988,1555 "9",15.7,1,9,6.5,6.2,0.553,95.5,39,28.6,0.081,2.8,4210,23.9,0.071697,29.4001,856 "10",14,0,11.8,7.1,6.8,0.632,102.9,7,1.5,0.1,2.4,5260,17.4,0.044498,19.5994,705 "11",12.4,0,10.5,12.1,11.6,0.58,96.6,101,10.6,0.077,3.5,6570,17,0.016201,41.6,1674 "12",13.4,0,10.8,7.5,7.1,0.595,97.2,47,5.9,0.083,3.1,5800,17.2,0.031201,34.2984,849 "13",12.8,0,11.3,6.7,6,0.624,97.2,28,1,0.077,2.5,5070,20.6,0.045302,36.2993,511 "14",13.5,0,11.7,6.2,6.1,0.595,98.6,22,4.6,0.077,2.7,5290,19,0.0532,21.501,664 "15",15.2,1,8.7,5.7,5.3,0.53,98.6,30,7.2,0.092,4.3,4050,26.4,0.0691,22.7008,798 "16",14.2,1,8.8,8.1,7.7,0.497,95.6,33,32.1,0.116,4.7,4270,24.7,0.052099,26.0991,946 "17",14.3,0,11,6.6,6.3,0.537,97.7,10,0.6,0.114,3.5,4870,16.6,0.076299,19.1002,539 "18",13.5,1,10.4,12.3,11.5,0.537,97.8,31,17,0.089,3.4,6310,16.5,0.119804,18.1996,929 "19",13,0,11.6,12.8,12.8,0.536,93.4,51,2.4,0.078,3.4,6270,13.5,0.019099,24.9008,750 "20",12.5,0,10.8,11.3,10.5,0.567,98.5,78,9.4,0.13,5.8,6260,16.6,0.034801,26.401,1225 "21",12.6,0,10.8,7.4,6.7,0.602,98.4,34,1.2,0.102,3.3,5570,19.5,0.0228,37.5998,742 "22",15.7,1,8.9,4.7,4.4,0.512,96.2,22,42.3,0.097,3.4,2880,27.6,0.089502,37.0994,439 "23",13.2,0,9.6,8.7,8.3,0.564,95.3,43,9.2,0.083,3.2,5130,22.7,0.0307,25.1989,1216 "24",13.1,0,11.6,7.8,7.3,0.574,103.8,7,3.6,0.142,4.2,5400,17.6,0.041598,17.6,968 "25",13,0,11.6,6.3,5.7,0.641,98.4,14,2.6,0.07,2.1,4860,19.6,0.069197,21.9003,523 "26",13.1,0,12.1,16,14.3,0.631,107.1,3,7.7,0.102,4.1,6740,15.2,0.041698,22.1005,1993 "27",13.5,0,10.9,6.9,7.1,0.54,96.5,6,0.4,0.08,2.2,5640,13.9,0.036099,28.4999,342 "28",15.2,0,11.2,8.2,7.6,0.571,101.8,10,7.9,0.103,2.8,5370,21.5,0.038201,25.8006,1216 "29",11.9,0,10.7,16.6,15.7,0.521,93.8,168,8.9,0.092,3.6,6370,15.4,0.0234,36.7009,1043 "30",16.6,1,8.9,5.8,5.4,0.521,97.3,46,25.4,0.072,2.6,3960,23.7,0.075298,28.3011,696 "31",14,0,9.3,5.5,5.4,0.535,104.5,6,2,0.135,4,4530,20,0.041999,21.7998,373 "32",12.5,0,10.9,9,8.1,0.586,96.4,97,8.2,0.105,4.3,6170,16.3,0.042698,30.9014,754 "33",14.7,1,10.4,6.3,6.4,0.56,97.2,23,9.5,0.076,2.4,4620,23.3,0.049499,25.5005,1072 "34",12.6,0,11.8,9.7,9.7,0.542,99,18,2.1,0.102,3.5,5890,16.6,0.040799,21.6997,923 "35",12.3,0,10.2,9.7,8.7,0.526,94.8,113,7.6,0.124,5,5720,15.8,0.0207,37.4011,653 "36",15,0,10,10.9,9.8,0.531,96.4,9,2.4,0.087,3.8,5590,15.3,0.0069,44.0004,1272 "37",17.7,1,8.7,5.8,5.6,0.638,97.4,24,34.9,0.076,2.8,3820,25.4,0.045198,31.6995,831 "38",13.3,0,10.4,5.1,4.7,0.599,102.4,7,4,0.099,2.7,4250,22.5,0.053998,16.6999,566 "39",14.9,1,8.8,6.1,5.4,0.515,95.3,36,16.5,0.086,3.5,3950,25.1,0.047099,27.3004,826 "40",14.5,1,10.4,8.2,7.4,0.56,98.1,96,12.6,0.088,3.1,4880,22.8,0.038801,29.3004,1151 "41",14.8,0,12.2,7.2,6.6,0.601,99.8,9,1.9,0.084,2,5900,14.4,0.0251,30.0001,880 "42",14.1,0,10.9,5.6,5.4,0.523,96.8,4,0.2,0.107,3.7,4890,17,0.088904,12.1996,542 "43",16.2,1,9.9,7.5,7,0.522,99.6,40,20.8,0.073,2.7,4960,22.4,0.054902,31.9989,823 "44",13.6,0,12.1,9.5,9.6,0.574,101.2,29,3.6,0.111,3.7,6220,16.2,0.0281,30.0001,1030 "45",13.9,1,8.8,4.6,4.1,0.48,96.8,19,4.9,0.135,5.3,4570,24.9,0.056202,32.5996,455 "46",12.6,0,10.4,10.6,9.7,0.599,98.9,40,2.4,0.078,2.5,5930,17.1,0.046598,16.6999,508 "47",13,0,12.1,9,9.1,0.623,104.9,3,2.2,0.113,4,5880,16,0.052802,16.0997,849 "","teamID","yearID","lgID","G","W","L","R","RA" "1","ANA",2001,"AL",162,75,87,691,730 "2","ARI",2001,"NL",162,92,70,818,677 "3"
Answered 1 days AfterAug 13, 2021

Answer To: Please ensure the directions are specifically followed. Each problem requires the...

S answered on Aug 14 2021
141 Votes
1.
a) A simple linear regression model is fitted to predict the percentage of wins a team will end up with dependent variable Win Percentage (W/(W + L)) and independent variable Run Differential (R−RA).
In the outputs R_RA represents Run Differential and W_W_L represents the win percentage.
    Model
Summary
    Model
    R
    R Square
    Adjusted R Square
    Std. Error of the Estimate
    1
    .936a
    .875
    .875
    .025359962950
    a. Predictors: (Constant), R_RA
    ANOVAa
    Model
    Sum of Squares
    df
    Mean Square
    F
    Sig.
    1
    Regression
    2.433
    1
    2.433
    3782.529
    .000b
    
    Residual
    .346
    538
    .001
    
    
    
    Total
    2.779
    539
    
    
    
    a. Dependent Variable: W_W_L
    b. Predictors: (Constant), R_RA
    Coefficientsa
    Model
    Unstandardized Coefficients
    Standardized Coefficients
    t
    Sig.
    95.0% Confidence Interval for B
    
    B
    Std. Error
    Beta
    
    
    Lower Bound
    Upper Bound
    1
    (Constant)
    .500
    .001
    
    458.152
    .000
    .498
    .502
    
    R_RA
    .001
    .000
    .936
    61.502
    .000
    .001
    .001
    a. Dependent Variable: W_W_L
By using SPSS, the model is fitted and it can be expressed as:

where,
= Win Percentage

x=Run Differential
A scatterplot is drawn for the given data and it is as follows:
For testing the significance of slope;
The hypothesis to test the significance of the slope can be stated as:
The null hypothesis is there is no linear relationship between Win Percentage and Run Differential.
 i.e. H0:
The alternative hypothesis is there is a linear relationship between Win Percentage and Run Differential.
 i.e. H1:
The test statistic can be calculated using the formula;
where 
= Fitted slope value
=Standard error of slope. This can be calculated as:

By using the above formula, the test statistic value is calculated and it t=61.502 and using the t-distribution the p-value is obtained as 0.000.Thus, there exist a significant a linear relationship between Win Percentage and Run Differential.
The model is validated using the residual plot:
Here, it can be seen that the residual plot is mostly showed a random pattern and hence the assumptions of regression like independence of errors, constant variance are satisfied.
b) A simple linear regression model is fitted to predict the percentage of wins a team will end up with dependent variable Win Percentage (W/(W + L)) and independent variable Wpct.
    Model Summaryb
    Model
    R
    R Square
    Adjusted R Square
    Std. Error of the Estimate
    1
    .935a
    .874
    .874
    .025494917905
    a. Predictors: (Constant), R2
    b. Dependent Variable: W_W_L
    ANOVAa
    Model
    Sum of Squares
    df
    Mean Square
    F
    Sig.
    1
    Regression
    2.429
    1
    2.429
    3736.910
    .000b
    
    Residual
    .350
    538
    .001
    
    
    
    Total
    2.779
    539
    
    
    
    a. Dependent Variable: W_W_L
    b. Predictors: (Constant), R2
    Coefficientsa
    Model
    Unstandardized Coefficients
    Standardized Coefficients
    t
    Sig.
    95.0% Confidence Interval for B
    
    B
    Std. Error
    Beta
    
    
    Lower Bound
    Upper...
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