Question

Run a regression analysis to predict mpg based on weight and horsepower. What is the model’s predictive power, interpretation of each of the regression coefficients and their confidence intervals and use it in prediction?

MPG   Horsepower   Weight
43.1   48   1985
19.9   110   3365
19.2   105   3535
17.7   165   3445
18.1   139   3205
20.3   103   2830
21.5   115   3245
16.9   155   4360
15.5   142   4054
18.5   150   3940
27.2   71   3190
41.5   76   2144
46.6   65   2110
23.7   100   2420
27.2   84   2490
39.1   58   1755
28.0   88   2605
24.0   92   2865
20.2   139   3570
20.5   95   3155
28.0   90   2678
34.7   63   2215
36.1   66   1800
35.7   80   1915
20.2   85   2965
23.9   90   3420
29.9   65   2380
30.4   67   3250
36.0   74   1980
22.6   110   2800
36.4   67   2950
27.5   95   2560
33.7   75   2210
44.6   67   1850
32.9   100   2615
38.0   67   1965
24.2   120   2930
38.1   60   1968
39.4   70   2070
25.4   116   2900
31.3   75   2542
34.1   68   1985
34.0   88   2395
31.0   82   2720
27.4   80   2670
22.3   88   2890
28.0   79   2625
17.6   85   3465
34.4   65   3465
20.6   105   3380
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      

Answer 1

Result:

Run a regression analysis to predict mpg based on weight and horsepower. What is the model’s predictive power, interpretation of each of the regression coefficients and their confidence intervals and use it in prediction?

Excel used for calculations.

Regression Analysis
Regression Statistics
Multiple R	0.8657
R Square	0.7494
Adjusted R Square	0.7388
Standard Error	4.1766
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	2	2451.9737	1225.9869	70.2813	0.0000
Residual	47	819.8681	17.4440
Total	49	3271.8418
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	58.1571	2.6582	21.8780	0.0000	52.8094	63.5048
Horsepower	-0.1175	0.0326	-3.6003	0.0008	-0.1832	-0.0519
Weight	-0.0069	0.0014	-4.9035	0.0000	-0.0097	-0.0041

The estimated regression line is

MPG = 58.1571 - 0.1175*Horsepower- 0.0069*Weight

R square = 0.7494.

74.94% of variance in MPG is explained by the model.

When horsepower increases by 1 unit, the MPG decreases by 0.1175. Horse power significantly related to MPG, t=-3.6003, P=0.0008.

When weight increases by 1 unit, the MPG decreases by 0.0069. weight significantly related to MPG,      t =-4.9035, P=0.0000.