MATH 533 Course Project Part C Regression Model Keller 2023

MATH 533 Course Project Part C Regression Model Keller 2023. The correlation coefficient between sales and calls is calculated as 0.871. This positive correlation coefficient tells us that as the number of calls increase so does the number of sales. Correlation: Sales, Calls (Appendix III) Minitab Result Pearson correlation of Sales and Calls = 0.871 P-Value = 0.000 4. Minitab Result: (See above Fitted Line Plot for below result) S = 2.05708 R-Sq = 75.9% R-Sq(adj) = 75.7% The coefficient of determination, R-sq, is 75.9%. It gives us the proportion of the dependant variable. Sales can be explained by the number of calls. 5. H0: (Null Hypothesis) – There is not significant correlation H1: (Alternate Hypothesis)- There is correlation either negative or positive. Significance Level, α = 0.05 Decision Rule: This p-value is less than significant value (.05). Thus, the null hypothesis should be rejected. We accept the alternative hypothesis that sales are not equal to zero. It can be conclude that the regression model is valid due to overall test of significance. Math 4 Minitab Result General Regression Analysis: SALES versus CALLS (Appendix IV) Regression Equation SALES = 9.63795 + 0. CALLS Coefficients Term Coef SE Coef T P 95% CI Constant 9.63795 1.87156 5.1497 0.000 (5.92391, 13.3520) CALLS 0.20175 0.01148 17.5797 0.000 (0.17898, 0.2245) 6. There exist a strong positive relationship (R-sq=+0.871) between sales and calls. Calls are a good predictor for forecasting of sales. We can be nearly 100% sure that a relationship exist between calls and sales. 7. The 95% confidence interval for beta -1 is 0.17898, 0.2245. It tells us that we can be 95% confident that for each additional call, on average, sales are going to go up between 0.17898 and 0.2245. 8. WE can be 95% confident that average weekly sales will be between 39.4084 and 40.3932 when 150 calls are made. The interval is calculated on the basis of 95% confidence interval to estimated average weekly sales on the basis of weekly 150 calls. Mini Tab Output (Appendix – V) Prediction for Sales Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI Math 5 1 39.9008 0. (39.4084, 40.3932) (35.7890, 44.0126) Values of Predictors for New Observations New Obs CALLS 1 150 9. The predicted weekly sales of an individual will lie between 35.7890 and 44.0126 interval. This is calculated at a 95% confidence level with 150 calls being made. See above for Mini Tab Output. 10. We cannot make a prediction because 300 calls are outside the range of independent variables. Our maximum data is 210 calls; 300 would be an extreme outlier in the predictors. 11. Regression Equation: SALES = 8.60864 + 0.20551 CALLS + 0. TIME - 0. YEARS For each additional call sales will go up by 0.20551; holding constant time and years. Minitab Result - Appendix -VI General Regression Analysis: SALES versus CALLS, TIME, YEARS Regression Equation Math 6 SALES = 8.60864 + 0.20551 CALLS + 0. TIME - 0. YEARS Coefficients Term Coef SE Coef T P 95% CI Constant 8.60864 3.55193 2.4236 0.017 ( 1.55811, 15.6592) CALLS 0.20551 0.01409 14.5811 0.000 ( 0.17753, 0.2335) TIME 0.05204 0.10570 0.4923 0.624 (-0.15778, 0.2619) YEARS -0.18179 0.16932 -1.0736 0.286 (-0.51789, 0.1543) Summary of Model S = 2.06152 R-Sq = 76.31% R-Sq(adj) = 75.57% PRESS = 442.906 R-Sq(pred) = 74.29% Analysis of Variance Source DF Seq SS Adj SS Adj MS F P Regression 3 1314.45 1314.45 438.151 103.097 0. CALLS 1 1307.75 903.56 903.561 212.609 0. TIME 1 1.81 1.03 1.030 0.242 0. YEARS 1 4.90 4.90 4.899 1.153 0. Error 96 407.99 407.99 4.250 Total 99 1722.44 12. The low P-value tells us that at least on variable is significant. We can reject the null hypothesis, H0: B1=B2=B3=0 versus Ha: At least one of the B1, B2, B3 is not equal to 0 Significance Level, α = 0.05 General Regression Analysis: SALES versus CALLS, TIME, YEARS Regression Equation SALES = 8.60864 + 0.20551 CALLS + 0. TIME - 0. YEARS