Question

	Credit Score	Age	Income	Residence	Gender
Louise	546	20	$484	1	Female
Danielle	601	29	$936	18	Female
Mohan	610	36	$953	13	Male
Roger	829	65	$1,549	19	Male
Brad	643	36	$1,169	12	Male
John	652	34	$1,591	8	Male
Karim	787	62	$1,522	11	Male
Jasmine	669	40	$1,202	9	Female
Emily	775	55	$1,873	5	Female
Donna	688	49	$1,185	11	Female
Monique	740	54	$1,346	3	Female
Fred	690	44	$1,521	17	Male
Maria	710	49	$1,316	13	Female
Dennis	720	48	$1,738	11	Male
Oliver	725	56	$1,201	15	Male

Determine the regression model to predict Credit Score based on the four independent variables. Interpret the coefficients

Is the regression significant at 5%? Which independent variable is the most significant?

What is the coefficient of determination? interpret

Answer 1

Regression is performed using using Excel Data Analysis Toolpack.

Following is the output for the Fitted Regression Model :

Interpretation of coefficients :

Coefficient corresponding to Age variable = 4.928 which means that with one unit increase in the value of Age , there is an average increase of 4.928 in the value of Credit score.

Coefficient corresponding to Income variable = 0.05 which means that with one unit increase in the value of Income , there is an average increase of 0.05 in the value of Credit score.

Coefficient corresponding to Residence variable = - 0.13829 which means that with one unit increase in the value of Residence , there is an average decrease of 0.13829 in the value of Credit score.

Coefficient corresponding to Gender variable = - 5.076 which means that for Male people , there is an average decrease of - 5.076 in the value of Credit score.

So, we can see from the above Table that P-value corresponding to variables - Age and Income is less than 0.05 ( Level of significance) , therefore we can say that Age and Income are statistically significant variables in the fitted regression model. Whereas, P-value corresponding to variables - Residence and Gender is greater than 0.05 ( Level of significance) , therefore we can say that Residence and Gender are not statistically significant variables in the fitted regression model.

Now, we consider the value of " Significance F " in the ANOVA table , which is 7.7968 E-08 < 0.05 ( Level of significance) we can conclude that Overall Regression is significant at 5 % level of significance.

Independent variable " Age " is most significant because the P-value corresponding to Age variable is lowest as compared to all other 3 variables.

Coefficient of determination = R-square = 0.973411155 = 97.34 % (approx)

This means that 97.34% of the total variation in the dependent variable is being explained by the 4 independent variables considered in the model.