Marijuana (%) 3) (1 point each) An online clothing retailer keeps track of its customers' 1400 purchases. For those customers who signed up for the company's credit card, 1200 the company also has information on the customers' Age and Income. A random sample of 500 of these customers shows the scatterplot of Total 1000 Yearly Purchases by income (shown to the right). The correlation between 800 Total Yearly Purchases ( Total Yearly Purchases and Income is 0.722. Summary statistics for the two 600 variables are: 400 200 Mean Std. Dev. Income $50,343.40 $16,952.50 Total Yearly Purchase $572.52 $253.62 20 30 40 50 60 70 80 Income (thousands of dollars) a) What is the linear regression equation for predicting Total Yearly Purchases from income? b) Do the assumptions and conditions for regression appear to be met? c) What is the predicted Total Yearly Purchase for someone with a yearly Income of $20,000? For someone with a yearly Income of $80,000? d) What percent of the variability in Total Yearly Purchase is accounted for by this model? e) Do you think the regression might be a useful one for the company? Why? 4) (4 points) Each of the following scatterplots shows a cluster of points and one "stray" point. For each, answer these questions: 1) In what way is the point unusual? Does it have high leverage, a large residual, or both? a ) 2) Do you think that point is an influential point? 3) If that point were removed, would the correlation become stronger or weaker? Explain. 4) If that point were removed, would the slope of the regression line increase or decrease? b)