Study order Confirmat X Xavier University Student Hu x Module 5: Regression Mode
ID: 3227047 • Letter: S
Question
Study order Confirmat X Xavier University Student Hu x Module 5: Regression Modeli c ezto mheducation.com/hm.tpx os fiT ORGANIC produ... (1) alexewaylens..... Question 21 (of 220 An analyst studies quarterly data on the relationship between retail sales ly, in millions), gross national product (x, in billions), and a quarterly dummy d that equals 1 if the sales are for the 4th quarter, 0 otherwise. He estimates the model y Ao B1x Bzd B3xd e. Relevant regressiormesults are shown in the accompanying table. Coefficients Standard Error t Stat p value Intercept 186553.3 56421.1 3.31 0.0021 4.6 12.08 0.0000 55.0 112605.8 117053.0 0.96 0,3424. 9.3 -0.50 0.6178 a 1. Interpret the dummy variable, d. O At x 0, predicted 4th quarter sales are greater than other quarters by about $112,605.80 million. O At x 0, predicted 4th quarter sales are greater than other quarters by about $186,553,30 million. O At x o, predicted 4th quarter salos are greater than other quarters by about S299,159,10 million. O At x 0, predicted 4th quarter sales are less than other quarters by about S186,553.30 million. a 2. Is the dummy variable d significant at the 5% level? Yes, since we reject the relevant null hypothesis. O Yes, since we do not reject the relevant null hypothesis. No, since we reject the relevant null hypothesis, No, since we do not reject the relevant null hypothesis.Explanation / Answer
When we pluge x = 0 in the above regression model then we get, y = b0 + b2d + e and for fourth quarter we have given that the dummy variable d = 1, so the change in mean of dependent variable (y) is corresponding to the slope of dummy variable d, so the correct answer is
At x = 0 , predicted 4th quarter sales are greater than other quarters by about $122,605.80 million.
dummy variable d significant at 5% level
here p-value of dummy variable is 0.3424 > the given level of significant, so we do not reject the relevant null hypothesis, Hence correct choice of answer is
No, since we do not reject the relevant the null hypothesis at 5% level of significant
b-1) For fourth quarter we have given that the dummy variable d = 1, and change in x is one unit (that is $1 billion) and so the change in mean of dependent variable (y) is corresponding to the slope of dummy variable d and slope of the x variable that is (b1 + b3) = 55 + ( - 4.7) = 51.3, so the correct answer is last option d)
b-2) The p-value of interaction > 0.05 so we fail to reject null hypothesis and conclude that there is no significance effect of interaction at 5% level of significance.
So the current option is d) No, since we do not reject the relevant null hypothesis.