Question

The accompanying data are x = advertising share and y = market share for a particular brand of cigarettes during 10 randomly selected years.

x	0.104	0.072	0.072	0.077	0.086	0.047	0.060	0.050	0.070	0.052
y	0.137	0.128	0.122	0.086	0.079	0.076	0.065	0.059	0.051	0.039

(a) Calculate the equation of the estimated regression line. (Round your answers to six decimal places.)
y =

Obtain the predicted market share when the advertising share is 0.09. (Round your answer to five decimal places.)


(b) Compute r². (Round your answer to three decimal places.)


(c) Calculate a point estimate of σ. (Round your answer to four decimal places.)


On how many degrees of freedom is your estimate based?

Answer 1

Here the dependent variable is market share for a particular brand of cigarettes during 10 randomly selected years and independent variable is advertising share.

This is the problem of simple linear regression.

We can do regression in excel.

steps :

ENTER data into excel sheet --> Data --> Data analysis --> Regression --> ok --> Input Y range : select range of y --> Input X range : select range of x --> Labels --> Output range : select one empty cell --> ok

a) Calculate the equation of the estimated regression line. (Round your answers to six decimal places.)

The regression equation is,

y = -0.003790 + 1.275249*x

(b) Compute r2. (Round your answer to three decimal places.)

R2 = 0.440

It expresses the proportion of variation in y which is explained by variation in x.

c) Calculate a point estimate of σ. (Round your answer to four decimal places.)

σ = 0.0269

On how many degrees of freedom is your estimate based?

Degrees of freedoms = n-2 = 10-2 = 8

Output :

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.663698
R Square	0.440495
Adjusted R Square	0.370557
Standard Error	0.026946
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.004573	0.004573	6.298352	0.036391
Residual	8	0.005809	0.000726
Total	9	0.010382
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.00379	0.036082	-0.1051	0.918885	-0.087	0.079413	-0.087	0.079413
x	1.275249	0.508138	2.509652	0.036391	0.103481	2.447017	0.103481	2.447017