A regression equation is used to predict local consumers\' total yearly purchase

Question

A regression equation is used to predict local consumers' total yearly purchases on clothing dependent on their income. The following statistics are given: Mean SD Income $95,000 $12,000 Spending on Clothing $4,000 $750 r (Income, Spending) -0.6 (a) what is the percentile of expected spending for someone in the top 20% of income (b) Rcan be inferred from r. Comment on the strength of the relationship and what is earners? left unexplained Comment on other variables that could be used on a data set of individuals to help predict spending on clothing?

Explanation / Answer

a) Slope = 0.6*750/12000 = 0.0375

Intercept = 4000-0.0375*95000 = 437.5

Equation

Spending = 0.0375*Income+437.5

b) r^2 =0.6*0.6 = 0.36 or 36%, so 36% of variability is explained and 64% remain unexplained

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