Question

Question 5 (25pts) Suppose the athletic director at a university would like to develop a regression model to predict the point differential for games played by the men's basketball team. A point differential is the difference between the final points scored by two competing teams. A positive differential is a win, and a negative differential is a loss. For a random sample of games, the point differential was calculated, along with the number of assists, rebounds, turnovers, and personal fouls. Use the data in Q5data.xlsx to complete parts a through f below. Assume a=0.10. a) Construct a regression model using all four independent variables. (Round to three decimal places as needed.) b) Identify the general form of the null and alternative hypotheses. c) Find the test statistic for the coefficient of each independent variable. (Round to two decimal places as needed.) d) Determine the appropriate critical value(s) for a=0.10. (Round to three decimal places as needed.)

please show all the work. if you use excel please show the screenshots. Thank you !

Answer 1

go to data analysis> regrssion> ok>

B C D E F G Regression ? Х Input OK y x1 x2 3 X4 Input Y Range: $B$3:$B$13 1 Cancel 1 10 18 17 26 Input X Range: $C$3:$F$13 1 16 12 17 15 Help 12 23 -7 14 30 13 15 Constant is Zero Labels Confidence Level: 8 12 18 22 95 %6 13 16 12 13 12 12 17 5 8 14 Output options 2 4 20 20 20 $F$18 1 Output Range: 17 13 30 15 26 -5 8 12 15 21 9 9 17 11 19 O New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Plots Line Fit Plots Normal Probability Normal Probability Plots

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.973513
R Square	0.947728
Adjusted R Square	0.90591
Standard Error	2.938593
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	4	782.8234	195.7058	22.66339	0.002105
Residual	5	43.17665	8.635329
Total	9	826

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0.737988	8.134577	0.090722	0.931236	-20.1726	21.64858
x1	0.990378	0.291837	3.393602	0.019385	0.240188	1.740568
x2	0.929485	0.153401	6.059178	0.001767	0.535155	1.323815
x3	-0.39941	0.382229	-1.04495	0.343912	-1.38196	0.583143
x4	-0.75942	0.269283	-2.82016	0.037102	-1.45163	-0.06721

Y =0.738 +0.990*X1 +0.929*X2 -0.399*X3 -0.759*X4

........................

B)

Ho: b1=b2=b3=b4=0

Ho : atleast one of the coefficient is not equal to 0

.....................

c)

	Coefficients	Standard Error	t Stat
Intercept	0.738	8.134577	0.09
x1	0.990	0.291837	3.39
x2	0.929	0.153401	6.06
x3	-0.399	0.382229	-1.04
x4	-0.759	0.269283	-2.82

.........

d)

critical t-value =    2.0150   [excel function: =t.inv.2t(α,df) ]       
................

e)

	Coefficients			P-value
Intercept	0.738			0.931
x1	0.990			0.019
x2	0.929			0.002
x3	-0.399			0.344
x4	-0.759			0.037

............

f)

	Coefficients	Standard Error	t Stat	P-value	sig
Intercept	0.738	8.134577	0.09	0.931	not signifcant
x1	0.990	0.291837	3.39	0.019	significant
x2	0.929	0.153401	6.06	0.002	significant
x3	-0.399	0.382229	-1.04	0.344	not signifcant
x4	-0.759	0.269283	-2.82	0.037	significant

................

Please let me know in case of any doubt.

Thanks in advance!

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