Question

TULITULLI F1 x ✓ fx A B E F X2 34.5 | H I J K L L M N O P Question 15: Note that Y represents the dependent variable, X1 represents a categorical independent variable w/ three levels (A, B, C), and X2 represents a quantitative independent variable. Let a = 0.05. 1958 1679 22.6 1668 21.2 30.4 1876 1348 16.7 (a) Write out the estimated regression line (including all variables). Answer: yhat = (b) What is the adjusted coefficient of determination? Answer: (c) Predict Y for X1 = C and X2 = 31.2. 1385 15.9 22.7 1698 1943 35.6 Answer: 1678 22.6 (d) Run an overall F test to determine if the multiple regression model is significant. To receive full credit you must give me: 1496 17.6 (i) Test Statistic Answer: (ii) P-value Answer: (iii) Decision: Reject or Fail to Reject Ho? Answer: 24

Answer 1

B K 1 We will take A=1,B=2,C33 Regression Statistics 0.95 0.89 2 3 4 5 6 7 8 9 10 11 Α Y 1958 1679 1668 1876 1348 1385 1698 1943 1678 1496 X2 34.5 22.6 21.2 30.4 16.7 15.9 22.7 35.6 22.6 17.6 Multiple R R Square Adjusted R Square Standard Error Observations 0.86 75.51 9 2 3 2 2 1 3 df 2 F 25.55 Significance F 0.0012 Regression Residual Total ANOVA SSMS 291418.4 145709.2 34211.2 5701.867 325629.6 SE tStat 166.515.72 36.83 0.12 4.74 6.28 Intercept X1 Coefficients 952.79 4.59 29.73 P-value 0.00 0.90 0.00 Lower 95% 545.34 -85.53 18.15 Upper 95% 1360.23 94.72 41.32 X2 L a) The Regression Equation is Y=952.79+4.59*X1+29.73*X2 b) Coefficient of determination=R^2=0.89.

when X1=C=3, X2=31.2 Y=952.79+4.59*3+29.73*31.2, Yhat=1894.14 d) Test Statistics=25.55 P value=0.0012 Here, P value is less than 0.05. We reject the null hypothesis.