Question

1. Fit a multiple regression model using MPG as the dependent variable and DISP, HP, and WT as the independent variables.
2. Is the overall regression model significant? Test at the α = 0.05 level of significance. State the null hypothesis, the alternative hypothesis =, the test statistic calculated and critical values and your test conclusion.

mpg	disp	hp	wt
21	160	110	2.62
21	160	110	2.875
22.8	108	93	2.32
21.4	258	110	3.215
18.7	360	175	3.44
18.1	225	105	3.46
14.3	360	245	3.57
24.4	146.7	62	3.19
22.8	140.8	95	3.15
19.2	167.6	123	3.44
17.8	167.6	123	3.44
16.4	275.8	180	4.07
17.3	275.8	180	3.73
15.2	275.8	180	3.78
10.4	472	205	5.25
10.4	460	215	5.424
14.7	440	230	5.345
32.4	78.7	66	2.2
30.4	75.7	52	1.615
33.9	71.1	65	1.835
21.5	120.1	97	2.465
15.5	318	150	3.52
15.2	304	150	3.435
13.3	350	245	3.84
19.2	400	175	3.845
27.3	79	66	1.935
26	120.3	91	2.14
30.4	95.1	113	1.513
15.8	351	264	3.17
19.7	145	175	2.77
15	301	335	3.57
21.4	121	109	2.78

Answer 1

we will solve it by using excel and the steps are

Ener the Data into excel

Click on Data tab

Click on Data Analysis

select Regression

select input and output range

click on labels if your selecting data with labels

click on ok

The output from excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9093
R Square	0.8268
Adjusted R Square	0.8083
Standard Error	2.6389
Observations	32.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	3.0000	931.0565	310.3522	44.5655	0.0000
Residual	28.0000	194.9907	6.9640
Total	31.0000	1126.0472
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	37.1055	2.1108	17.5788	0.0000	32.7817	41.4293
disp	-0.0009	0.0103	-0.0905	0.9285	-0.0221	0.0203
hp	-0.0312	0.0114	-2.7245	0.0110	-0.0546	-0.0077
wt	-3.8009	1.0662	-3.5649	0.0013	-5.9849	-1.6169

a) Fit a multiple regression model using MPG as the dependent variable and DISP, HP, and WT as the independent variables.

so using above output we can write the regression equation

mpg=37.1055-0.0009disp-0.0312hp-3.8009wt

b) Is the overall regression model significant? Test at the α = 0.05 level of significance. State the null hypothesis, the alternative hypothesis =, the test statistic calculated and critical values and your test conclusion.

The null hypothesis,

Ho:

That is overall regression model is not significant

the alternative hypothesis

H1: At least one

That is overall regression model is significant.

test statistic

F-statistic =44.5655

Significance F= 0.0000

SinceSignificance F= 0.0000 <  α = 0.05 level of significance we reject the null hypothesis and conclude that the overall regression model significant.