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ID: 3310136 • Letter: T
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the fleet manager for a medium the fleet manager for a medium the fleet manager for a medium Question 5 (20 Points) Data on the Income and Age of executives at a well-known advertising firm was used to produce the following regression output. SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square 0.44607971 Standard Error 3.1784353 Observations 0.7941787 0.63071981 7 ANOVA MS F gnificance F Regression Residual Total 2 69.01876761 34.50938 3.415942 0.136368 4 40.40980382 10.10245 6 109.4285714 coefficients itandard Erro t Stat P-value Lower 95%Upper 95% 44.660119 29.74047838-1.50166 0.207592 -127.233 37.91269 5.26105625 2.343471318 2.244984 0.088134 -1.24546 11.76758 0.0939775 0.044915783 -2.0923 0.104558 -0.21868 0.030729 Intercept Age a. Write out the regression equation. b. Why do you think this particular regression model was developed? Explain carefully. c. Test the independent variables for significance in the regression at the 0.05 level. d. Test the overall model for significance at the 0.05 level. 31PageExplanation / Answer
(A)
We know that, the regression equation is Y = a + b*X
The regression equation is
Income = -44.660119 + 5.26105625*(Age)
(B)
The slope tells us that for every unit increase in age, the average income will increase by 5.26105625 units. a model like this will arise from a theoretical relationship. At other times, we will have no theoretical knowledge of the relationship between age and income, and the choice of the model is based on inspection of a regression table. We then think of the regression model as an empirical model. Thus, we think this particular regression model was developed.
(C)
The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis. Conversely, a larger (insignificant) p-value suggests that changes in the predictor are not associated with changes in the response.
Here, p-value of independent variable Age (=0.088134) is greater than given significance level p-value (=0.05). Thus, the age are not associated with changes in the income.
(D)
The p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 0.05) indicates that you can reject the null hypothesis. Conversely, a larger (insignificant) p-value suggests that changes in the predictor are not associated with changes in the response.
Here, p-value of the overall model (=0.136368) is greater than given significance level p-value (=0.05) at degree of freedom (2,4). Thus, the model is not significant at p < .05.
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