Question

Vore are in US (S Income Rate 80.7 67.9 72.0 73.5 73.4 78.7 69.5 Area 1000) AverageExpense($100 New York Los Angeles Chicago Boston Seattle 70.5 54.7 61.1 62.2 65.0 66.8 58.7 San Francisco Dallas Computed the value of bo and bi. Find the regression equation. Predict the income rate for an area with an average expense of $ Computed the Coefficient of correlation. Find the

Answer 1

The average expense is depends on income rate. Hence here average expense rate is dependent variable and income rate is independent variable.

We run regression analysis in excel and we get the output as :

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.963031
R Square	0.927428
Adjusted R Square	0.912914
Standard Error	1.551042
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	1	153.7199	153.7199	63.89741	0.000495
Residual	5	12.02865	2.40573
Total	6	165.7486
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-17.9276	10.10534	-1.77407	0.136232	-43.9042	8.049034	-43.9042	8.049034
Income rate	1.094615	0.136937	7.993585	0.000495	0.742608	1.446622	0.742608	1.446622

From out put we get ,

Intercept = b₀ = -17.9276 , b₁ = 1.0946

Hence the regression equation is given by

y = b0 + b1 *x

y = -17.9276 + 1.0946 b1

Here we are given y = 75 , so the income rate is given by

y = - 17.276 + 1.0946 * 75

= 64.819

The coefficient of ccorrelation is given by

r = 0.9630