Question PartPoints The accompanying data are x = advertising share and y = mark

Question

Question PartPoints

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

x 0.103 .072 .072 .077 .086 .047 .060 .050 .07 .052
y .136 .124 .120 .086 .079 .076 .065 .059 .051 .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 . (Round your answer to four decimal places.) 
 

On how many degrees of freedom is your estimate based? 

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -0.0039280688 + 1.2689125 x
Sample size: 10
R (correlation coefficient) = 0.67163638
R-sq = 0.45109543
Estimate of error standard deviation: 0.025918261

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) Regression line equation:

y = - 0.003928 + 1.268913 x

At x = 0.09, y = 0.11027

b) r2 = 0.451

c) Point estimate of = 0.0259

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

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -0.0039280688 0.035068534 0 8 -0.11201121 0.9136 Slope 1.2689125 0.49488111 0 8 2.5640754 0.0334

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