Question

(a) The following is taken from the output generated by an Excel analysis of expenditure data using multiple regression: Regression Statistics Multiple R 0.9280 0.8611 0.8365 Adjusted R2 Standard Error.1488 Observations21 ANOVA Source Regression Residual Total df MS Significance of F 1.66E-07 3 308.68 35.117 102.893 2.930 17 20 358.49 49.81 Coefficient Standard Error 6.2000 0.7260 0.7260 0.9500 t Stat 3.7097 0.2755 -2.0523 0.5158 23.00 0.20 Intercept X2 X3 0.49 (i) Find the limits of the 95 percent confidence interval for the coefficient of the variable X2. (4 marks) (ii) Using the t-distribution table, what can you say about the probability level at which the variable X2 should be included in the regression model? (4 marks) (iii) Explain what the R statistic tells you about this regression. (3 marks) (iv)State what would happen to R if a further explanatory variable was added to the three existing explanatory variables (2 marks) (v) Use the regression model to estimate the value of the dependent variable if (3 marks)

Answer 1

(i) = estimated coefficient of X,--149 se(β) = standard error of estimated coefficient of X2 = 07260 0.025,17 2.1098 95% C.1. for the coefficient of the variable X2 is 2 -to.o25,17 X se(B2), B2+to.025,17 x se(2) (-3.0217, 0.0417) (ii) p-value 2P(t > 2.0523|t ~ tr) = 0.0559 Since 0.05 < p- value 0.1 so at 10% level of significance X2 should be included in the regression model. (iii) = 0.8611-> 86.11% of total variation of response variable is explained by this regression equation iv) The value of R is increased if we add more explanatory variables. (v) At X1 1, X2-2, X3 3 then estimated value of dependent variable = 23-0.20 * 1-1.49 * 2-0.49 * 3 = 18.35 t17