Question

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.870402
R Square	0.7576
Adjusted R Square	0.68488
Standard Error	1816.52
Observations	27
ANOVA
	df	SS	MS	F	Significance F
Regression	6	2.06E+08	34376848	10.41804	2.81E-05
Residual	20	65994862	3299743
Total	26	2.72E+08
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-4695.4	12622.97	-0.37197	0.713825	-31026.5	21635.66	-31026.5	21635.66
AGE	161.7028	126.5655	1.277621	0.216015	-102.308	425.7137	-102.308	425.7137
MILAGE	-0.03441	0.023186	-1.4842	0.153346	-0.08278	0.013953	-0.08278	0.013953
HP	46.33786	10.27696	4.508908	0.000214	24.9005	67.77522	24.9005	67.77522
AUTOMATIC	-98.5413	1422.364	-0.06928	0.945455	-3065.54	2868.458	-3065.54	2868.458
WEIGHT	16.98936	10.20147	1.665385	0.111424	-4.29052	38.26925	-4.29052	38.26925
DOORS	-2073.7	1346.151	-1.54047	0.139121	-4881.72	734.3233	-4881.72	734.3233

1.What is the R² ?

2. Is the model linear?

3. Are all the independent variables good?

4. Which variable would you remove first?

5. A blank stepwise procedure puts the most significant variable in first, adds the next variable that will improve the model the most. A blank stepwise regression begins with all the independent variables and deletes the least helpful.

Answer 1

1. R-square is the % variation explained in the dependent variable. Here, R-square value = 75.76%

2. Yes, the model is linear as the degree of all the variables is 1.

3. We are looking for significance of the independent variables here or those who have a p-value < 0.05. Hence we can say that only the variable HP is significant at a significance level of 0.05. Rest of the variables are not significant.

4. We will remove the variable with the lowest t-statistic or the highest p-value (which is the least significant). Hence, in this case we will remove the variable AUTOMATIC with the lowest t-statistic having -0.06928

5. Here, we will go with all the independent variables but the AUTOMATIC variable which is the least helpful or the least significant.