Case 2 Instruction (3)

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Multiple Regression: Case Problem Predicting Winnings for Student Name: Course: Date:21/10/2023

Abstract Finding the best predictor of NASCAR drivers' earnings among Poles, wins, top5, and top 10 is the goal of this case study. Additionally, two additional variables the top 2–5 and top 6–10 will be developed. Multiple regression analysis will be performed in order to draw findings Introduction The case study's objective is to forecast NASCAR drivers' 2012 earnings utilizing a variety of factors, including Driver name, Points, Poles, Wins, Top 5,Top 10 Winnings ($),Top 2-5 number of times a driver finished in the top two- five during the season and Top 6-10- number of times a driver finished in the top six- ten during the season. Objectives: The purpose of the case study is to use multiple regression analysis to identify which variable best predicts a driver's earnings. The following inquiries will assist in decision-making: 1. Using simply the number of poles won (poles), victories (wins), number of top five finishes (Top 5) or number of top ten finishes (Top 10) as predictors, we will forecast earnings ($). The question is, which of these four variables better predicts winnings individually?

Coefficients Standard Error t Stat P-value Intercept 3140367.087 184229.0243 17.046 5.59454E-17 Poles -12938.9208 107205.0751 -0.12069 0.90473880 2 Wins 13544.81269 111226.2163 0.12177 7 0.90388757 Top 5 71629.39328 50666.86771 1.41373 2 0.16773416 3 Top 10 117070.5768 33432.88382 3.50166 0.00147031 4 Coefficients t Stat P-value Significance Intercept 3,140,367.09 17.04599533 5.59454E-17 Yes, < 0.05 Poles -12,938.92 -0.12069317 0.90474 No, > 0.05 Wins 13,544.81 0.12177716 0.90389 No, > 0.05 Top 5 71,629.39 1.413732416 0.16773 No, > 0.05 Top 10 117,070.58 3.501659548 0.00147 Yes, < 0.05 Top 10 P-value 0.0015 If p-value is very low, in this case (<0.05) then we reject the null hypothesis. Which means with 95% confidence we say that any change in Predictor variable has an effect on the response or dependent variable. For remaining variables (Poles,Wins,top5) as the p-value is greater than 0.05, we accept the null hypothesis that these variables has zero effect on the response variable From the above output, it can be observed that the p-value corresponding to t test each of the individual variables. It has been found that Top 10 finishes making the best predictor out of four (p-value = 0.0015

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Objective 2: Using the number of poles won (Poles), wins (Wins), top five finishes (Top 5), and top ten finishes (Top 10) as inputs, we will create an estimated regression equation that can be used to predict earnings ($). We will also test the equation for individual significance and talk about the results and conclusions. Earnings Vs Poles, wins, Top 5, Top 10 Regression equation: Winnings = 3,140,367.09 - 12,938.92 Poles + 13,544.81 Wins + 71,629.39 Top 5 + 117,070.58 Top 10 y = 3140367.09 − 12938.92 x 1 + 13544.81 x 2 + ¿ 71629.39 x 3 +117070.58 x 4 From the regression output, the p-values corresponding to poles, Wins, Top 5, Top 10 are 0.90474, 0.90389, 0.16773, 0.00147. At 0.05 level significance, number of Top 10 finishes seem to be significant. Objective 2: Using Poles, Wins, Top 2–5, Top 6–10, and additional independent variables, we will design an estimated model that may be used to forecast profits ($). We will test for individual significance and discuss our findings and conclusions.

SUMMARY OUTPUT Regression Statistics Multiple R 0.90580815 9 R Square 0.82048842 2 Adjusted R Square 0.79655354 4 Standard Error 581382.196 8 Observations 35 ANOVA df SS MS F Significance F Regression 4 4.63473E+13 1.15868E+1 3 34.2800348 2 8.61942E-11 Residual 30 1.01402E+13 3.38005E+11 Total 34 5.64875E+13 The estimated repression equation that can be used to predict Winnings ($) using Poles, Wins, Top 2-5 and Top 6-10 is, Winnings = 3140367-12939 Poles+202245 Wins + 188700 Top 2-5+117071 Top 6-10 Objective 4: Finally, we would suggest the estimated regression that is best suited to forecast earnings ($) based on the findings of our investigation. We would additionally offer an explanation of the equation's estimated regression coefficients.

Model 1 Coefficients Standard Error t Stat Intercept 3140367.087 184229.0243 17.046 Poles -12938.9208 107205.0751 -0.12069 Wins 13544.81269 111226.2163 0.12177 7 Top 5 71629.39328 50666.86771 1.41373 2 Top 10 117070.5768 33432.88382 3.50166 Winning (Y) = 3140367 - 12939*Poles+13545*wins+71629*Top5+117071*Top10 Model 2 Coefficients Standard Error t Stat Intercept 3140367.08 7 184229.0243 17.04599533 Poles -12938.9208 107205.0751 - 0.120693174 Wins 202244.782 8 90225.86834 2.241538779 Top 2-5 188699.970 1 34586.32226 5.455913141 Top 6-10 117070.576 8 33432.88382 3.501659548 Winning (Y) = 3140367 - 12939*Poles+202245*wins+188700*Top 2_5+117071*Top 6-10

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It is advised to use Model 2 rather than Model 1, which is based on the new variables.Every variable, with the exception of poles, is significant at the 5% level of significance and affects the response variable; in contrast, every variable in the first model, with the exception of the top 10, is unimportant. For the variables in model 2, the maximum correlation that we may see is less than 50%. However, all the variables in model 1 have a maximum correlation of 90%, indicating a high level of correlation. Model 2 has the most significant and least correlated variables, even if the adjusted R-sqr for both models is 79%. Thus It is better to use Model 2 than Model 1.