Question

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Could someone please give me some guidance on how to answer these, it's like looking at another language.

Thank you in advance

(a) Use the built regression tool in Excel and your personalized data set (see above) to estimate the simple regression of sales revenue in dollars (Y) generated by a salesperson in his/her first year of completed service on the salesperson’s aptitude test score (X). (2 marks)

When answering the following questions, assume all the assumptions of the neoclassical (stochastic regressor) simple regression (NSR) model with multivariate normally distributed random disturbances are satisfied.

(b) Clearly state your estimated conditional expectation function (sample regression line). Note that you do not need to estimate your equation manually, but rather you should simply write down your sample regression line using the estimated intercept and coefficient of X given in your summary regression output from Excel. (1 mark)

(c) With reference to your estimated equation, calculate (using a calculator) a 90% confidence interval for the coefficient (β2 ) of X in the model. In performing this calculation, use the relevant estimated standard error of the estimator of the coefficient of X given in your summary Excel regression output. Give an interpretation of the confidence interval you calculate. (2 marks)

(d) Again with reference to your estimated equation, perform a test of the null hypothesis that the coefficient (β2 ) of the aptitude test score of a salesperson equals zero against

the alternative that it is greater than zero, using the α = 0.05 (i.e. 5%) level of significance. In presenting your answer to this question you are required to use the 6- step hypothesis testing procedure given in the unit summary lecture notes. Again in answering this question, you should use the relevant estimated standard error of the estimator of the coefficient of X given in your summary Excel regression output. (3 marks)

(e) Give an interpretation of the realized coefficient of determination value (r2 ) given in your summary Excel regression output. (2 marks)

Answer 1

(a)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.78168639
R Square	0.611033613
Adjusted R Square	0.601309453
Standard Error	20116.232
Observations	42
ANOVA
	df	SS	MS	F	Significance F
Regression	1	25427653896	2.54E+10	62.83665	9.93216E-10
Residual	40	16186511599	4.05E+08
Total	41	41614165494
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 90.0%	Upper 90.0%
Intercept	117263.1332	6973.825793	16.81475	9.77E-20	103168.5055	131357.7609	105520.2496	129006.0169
X Variable 1	6884.587431	868.5031734	7.926957	9.93E-10	5129.277041	8639.897821	5422.157483	8347.01738

(b) Regression equation: У = 1 17263.1332+6884.5874X (c) 90% C.1. for β2: (5422.1575, 8347.0174) We are 90% confident that the slope of true regression lies betueen 5422.1575 and 8347.0174. (d) Null hypothesis, Ho : β2= 0 Alternative hypothesis, H1 : β2 > 0 Value of test statistic-t-7.9270 p - value P(t> 7.9270t400.0000<0.05. We reject Ho at 5% level. Now we conclude that slope is significantly greater than 0. (e) ? = 0.6110 i.e. 61.10% of total variation in Y is explained by the regression equation