46. Online clothes II For the online clothing retailer dis- cussed in the previo

Question

46. Online clothes II For the online clothing retailer dis- cussed in the previous problem, the scatterplot of Total Yearly Purchases by Income shows Here 1400 1200 1000 800 600 400F 200+ a) b) c) d) 20 30 40 50 60 70 80 Income (thousands of dollars) The correlation between Total Yearly Purchases and Income is 0.722. Summary statistics for the two variables are: Mean SD Income $50,343.40 $16,952.50 Total Yearly Purchase $572.52 $253.62 48. a) What is the linear regression equation for predicting Total Yearly Purchase from Income? pear to be met? for someone with a yearly Income of $20,000? For b) Do the assumptions and conditions for regression ap- c) What is the predicted average Total Yearly Purchase someone with an annual Income of $80,000? Purchases is accounted for by this model? the company? Comment. d) What percent of the variability in Total Yearly e) Do you think the regression might be a useful one for

Explanation / Answer

here dependent variable is Total Yearly Purchase (y) and independent variable Income (x)

(a) for regression equation y=a+bx=28.8113+0.0108*x

b=r*sd(y)/sd(x)=0.722*253.62/16952.50=0.0108

a=mean(y)-b*mean(x)=572.52-50343.4*0.0108=28.8113

(b) scatter plot shows sum linear trend so we can say that preliminary assumption met.

(c)for x=20000, y=28.8113+0.0108*20000=244.8113

for x=80000, y=28.8113+0.0108*80000=892.8113

(d) r=0.722, coefficient of determination for simple linear regression y=a+bx is given as

R2=r*r=0.722*0.722=0.5212

so 52.12% of variability explained by the indepenenet variable x in dependent variable y

(e) since R2=0.5212, it is quite well , so we can say that regression might be useful

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