The accompanying data are x = advertising share and y-market share for a particu

Question

The accompanying data are x = advertising share and y-market share for a particular brand of cigarettes during 10 randomly selected years. x 0.101 0.073 0.071 0.077 0.086 0.047 0.060 0.050 0.070 0.052 y 0.132 0.124 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 r^2. (c) Calculate a point estimate of sigma. (Round your answer to four decimal places.) On how many degrees of freedom is your estimate based? You may need to use the appropriate table in Appendix A to answer this question.

Explanation / Answer

a. Enter data in Excel-Data-Data Analysis-Regression-OK-enter B2:B11 in the Input Y range and A2:A11 in the Input X range-check Output range and type D3-click OK.

The summary output table display the coefficients of intercept(beta0) and slope(beta1). Substitute the values in the least sqaure regression equation:y=beta0+beta1x. Thus, the regression equation is:y=-0.002306+1.246086x

Substitute x with 0.09 in the regression equation and obtain the predicted market share.

yhat=-0.002306+1.246086(0.09)=0.10984

b) The coefficient of determination, R^2=0.425

c) The point estimate of sigma is s=sqrt [SSE/n-2]. Using the given output, s=sqrt[0.005480/(10-2)]=0.0262

The degrees of freedom is df=n-2=10-2=8

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