Stat 112 Notes 9 Addendum

Interpreting Multiple Regression Coefficients: Another Example A marketing firm studied the demand for a new type of personal digital assistant (PDA). The firm surveyed a sample of 75 consumers. Each respondent was initially shown the new device and then asked to rate the likelihood of purchase on a scale of 1 to 10, with 1 implying little chance of purchase and 10 indicating almost certain purchase. The age (in years) and income (in thousands of dollars) were recorded for each respondent. The data are in pda.JMP.

Simple Regressions to Predict Rating (Likelihood of Purchase) As income rises, the likelihood of purchase also increases; specifically a $10,000 increase in income is associated with a 0.7 increase in rating. As age increases, the likelihood of purchase also increases; specifically a 10-year increase in age is associated with a 0.9 increase in rating.

Multiple Regression For any fixed level of income, the average rating decreases by 0.7 if Age increases by 10 years. For all fixed income levels, old consumers have higher ratings on average than young consumers and at all fixed age levels, average ratings increase as income rises. Positive association between age and rating is a result of positive association between age and income.