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Suppose the following two estimated regression equations are obtained from monthly data on demand (y) of...

Suppose the following two estimated regression equations are obtained from monthly data on demand (y) of a product and its price (x), over n=11 months, in appropriate units: (a) 3x + 4y = 6 and (b) x + 3y = 3. One of these regression equations is obtained by regressing y on x and the other by regressing x on y.

(i) Calculate the correlation coefficient r between demand and price.

(ii) Calculate the absolute value of the estimated regression line slope for demand on price.

(iii) Calculate the sample (arithmetic) mean demand ybar .

(iv) Calculate the ratio of the sample standard deviation for demand to that for price.

(v) Suppose   Then, calculate the sample variance for price.

(vi). Calculate the coefficient of determination for the regression of price on demand.

(vii) Suppose sample variance for demand is 0.2040. Then calculate the estimated variance of the regression equation error for regressing demand on price.

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