Question

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.195389
R Square	0.038177
Adjusted R Square	0.037333
Standard Error	13.69067
Observations	1142
ANOVA
	df	SS	MS	F	Significance F
Regression	1	8481.255	8481.255	45.2492	2.74E-11
Residual	1140	213675.2	187.4344
Total	1141	222156.4
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	40.19631	0.596741	67.35967	0	39.02547	41.36714	39.02547	41.36714
X Variable 1	7.31E-05	1.09E-05	6.726752	2.74E-11	5.18E-05	9.45E-05	5.18E-05	9.45E-05

2. Discuss the statistical significance of the model as whole using the appropriate regression statistic at a 95% level of confidence.
3. Discuss the statistical significance of the coefficient for the independent variable using the appropriate regression statistic at a 95% level of confidence.
4. Interpret the coefficient for the independent variable.

What percentage of the observed variation in a person’s income is explained by the model?

5. Predict the value of a person’s income who is 45 years old, using this regression model.

Answer 1

b ]

From the ANOVA table given above, value of F-statistics is, 45.2492 and have P-value 2.74E-11.Therefore, at a 95% level of confidence our level of significance α = 5%

that is α =0.05

Hence, P-value =2.74*e^-11 < α =0.05  

We reject H0 because there is strong evidence against H0 and conclude that, model is significantly fitted to the data .

C]

Here, standard error for x-variable (Age) is 1.09E-05 is small indicating less deviation between the observsd and fitted value. Also t-test for regressor gives test statistics value 6.726752 with p-value 2.74E-11.

Hence, P-value < 0.05, We do reject H0 because there is strong evidence against H0 and conclude that, that regression coefficient will be significantly affect on the model.

d]

Here, adjusted R² =0.037333 , which indicates 3.7% percent of the observed variation in a person’s income is explained by the model.

e]

From the table,our regression equation is,

Person’s income= β0+ β1*Age

                            = 40.19631 + 7.31E-05*Age

To predict the value of a person’s income who is 45 years old, using this regression model,

      Person’s income = 40.19631 + 7.31E-05*40

                            =40.1992