Question

a) Find the multiple regression equation using all three explanatory variables. Assume that X1 is mid-term score, X2 is hours studying per week and x3 is hours watching television per week. Give your answers to 3 decimal places. û = mid-term score + hours studying + hours watching television + b) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis rejected. c) The explanatory variable that is most correlated with final score is: O mid-term score O hours studying per week O hours watching television per week d) The explanatory variable that is least correlated with final score is: O mid-term score O hours studying per week O hours watching television per week e) The value of R2 for this model, to 3 decimal places, is equal to f) The value of s for this model, to 3 decimal places, is equal to g) Construct a new multiple regression model by removing the variable average hours spent watching television per week. Give your answers to 3 decimal places. The new regression model equation is: + û = mid-term score + hours studying h) In the new model compared to the previous one, the value of R2 (to 3 decimal places) is: O increased O decreased unchanged i) In the new model compared to the previous one, the value of s (to 3 decimal places) is: O increased O decreased Ounchanged

Answer 1

a) Find the multiple regression equation using all three explanatory variables. Assume that X1 is mid-term score, X2 is hours studying per week and x3 is hours watching television per week. Give your answers to 3 decimal places. = 0.930 mid-term score + 0.575 hours studying + 0.211 hours watching television -9.062 + rejected. b) At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis ( is This is because pvalue is <0.05 c) The explanatory variable that is most correlated with final score is: pvalue= 0.000 pvalue of midterm score is least pvalue O mid-term score Intercept 0.096 hours studying per week Mid term 0.000 hours per 0.062 hours watching television per week hours wat 0.232 d) The explanatory variable that is least correlated with final score is: pvalue is the highest O mid-term score O hours studying per week O hours watching television per week e) The value of R2 for this model, to 3 decimal places, is equal to 0.923 f) The value of s for this model, to 3 decimal places, is equal to 6.663 g) Construct a new multiple regression model by removing the variable average hours spent watching television per week. Give your answers to 3 decimal places. The new regression model equation is: = -5.777 + 0.938 mid-term score + 0.630 hours studying h) In the new model compared to the previous one, the value of R2 (to 3 decimal places) is: R Square 0.918 O increased O decreased unchanged i) In the new model compared to the previous one, the value of s (to 3 decimal places) is: O increased decreased Ounchanged Standard 6.724

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SUMMARY OUTPUT
Regression Statistics
Multiple R	0.961
R Square	0.923
Adjusted R Square	0.914
Standard Error	6.663
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	3	13793.710	4597.903	103.578	0.000
Residual	26	1154.156	44.391
Total	29	14947.867
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-9.062	5.241	-1.729	0.096	-19.835	1.712
Mid term score	0.930	0.056	16.620	0.000	0.815	1.045
hours per week	0.575	0.295	1.948	0.062	-0.032	1.181
hours watchin tv	0.211	0.173	1.224	0.232	-0.144	0.567
	pvalue
Intercept	0.096
Mid term score	0.000
hours per week	0.062
hours watchin tv	0.232
SUMMARY OUTPUT
Regression Statistics
Multiple R	0.958
R Square	0.918
Adjusted R Square	0.912
Standard Error	6.724
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	2	13727.18	6863.589	151.8135	2.05E-15
Residual	27	1220.688	45.21067
Total	29	14947.87
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-5.777	4.544	-1.271	0.214	-15.101	3.546
Mid term score	0.938	0.056	16.699	0.000	0.823	1.053
hours per week	0.630	0.294	2.140	0.042	0.026	1.233

Excel instructions are as follows

E F H K х Regression 36 Input Input Y Range: OK 44 $A$1:$A$31 А B D 1 Final scored term sccurs per wears watchin tv 2 33 9 27 3 94 93 12 4 17 24 5 64 18 31 6 28 26 14 18 7 69 69 11 27 8 56 68 19 9 52 6 15 41 76 Cancel Input X Range: $B$1:$D$31 Help Labels Confidence Level: Constant is Zero 95 % 12 50 10 82 89 15 17 SG$28 11 94 97 14 17 12 38 43 18 19 Output options Output Range: New Worksheet Ply: New Workbook Residuals Residuals Standardized Residuals 13 66 65 16 28 14 50 52 4 12 15 45 48 14 28 Residual Plots Line Fit Plots 16 86 99 13 23 17 34 38 11 9 Normal Probability Normal Probability Plots 18 73 61 19 21 19 34 44 6 19