Coefficients SE Coef Term Constant INCOME GENDER W 1 INCOME GENDER W 1 -0.021 Co
ID: 3065734 • Letter: C
Question
Coefficients SE Coef Term Constant INCOME GENDER W 1 INCOME GENDER W 1 -0.021 Coef 3.487 0.415 1.131 0.251 13.872 0.000 0.004 106.280.00 0.697 0.006 1.623 0.119 (c) The Minitab output above gives the results of our model based on data from n-26 individuals. Let's conduct the t-test to see if there is significant interaction between the two predictors, income and gender. Namely, we will test Ho : 3 = 0 vs. Ha : 3 0 i. Find the test statistic and a range for the p-value based on the test statistic. ii. State the conclusion for this test. (d) As the Minitab output shows, the p-value for the t-test for Gender (2) is 0.119. Does this mean that we should conclude that Gender is not significant and remove this pre- dictor from our model? Explain (e) What is the predicted price of a vehicle for a woman who has income of $60,000? (f) What is the predicted price of a vehicle for a man who has income of $60,000?Explanation / Answer
(c)
(i) Here the given test is two tailed test.
Test staistic
t = ^3/se(^3) = -0.021/0.006 = -3.5
Here dF = 26 -2 = 24 and alpha = 0.05
p - value = TDIST (l t l > 3.5 ; 24 ; two tailed) = 0.001842 < 0.05 ; Here we can see the range of p -values is in between 0.01 to 0.001
so we will reject the null hypothesis and conclude that there is significant interacion between the two predictors.
(d) Here as the minitiab output show that p - vlaue for the test test for the Gender is 0.119. Yes that mean that we should conclude that the independent variable Gender is not significant here and we may remove the predictor from the the model.
(e) Here women = 1 and income = $ 60000
y^( Price of car owner) = 4.618 + 0.394 * income
= 4.618 + 0.394 * 60 = 28.258 (in 1000units)
(f) For men = 0 and income = $ 60000