Abby Kratz, a market specialist at the market research firm of Saez, Sikes, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is weekly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighborhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table. $$\begin{array} { | c | c | c | c | c | }
\hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \
\hline \text { Intercept } & 19.68247 & 10.01176 & 1.965934 & 0.077667 \
\hline x _ { 1 } \text { (income) } & 1.735272 & 0.174564 & 9.940612 & 1.68 \mathrm { E } - 06 \
\hline x _ { 2 } \text { (neighborhood) } & 49.12456 & 7.655776 & 6.416667 & 7.67 \mathrm { E } - 05 \
\hline
\end{array}$$ For what annual income will a suburban household and a rural household have the same predicted weekly grocery spending?

Question

Abby Kratz, a market specialist at the market research firm of Saez, Sikes, and Spitz, is analyzing household budget data collected by her firm.Abby's dependent variable is weekly household expenditures on groceries (in $'s), and her independent variables are annual household income (in $1,000's)and household neighborhood (0 = suburban, 1 = rural).Regression analysis of the data yielded the following table. $$\begin{array} { | c | c | c | c | c | } 
\hline & \text { Coefficients } & \text { Stardard Error } & t \text { Statistic } & p \text {-value } \
\hline \text { Intercept } & 19.68247 & 10.01176 & 1.965934 & 0.077667 \
\hline x _ { 1 } \text { (income) } & 1.735272 & 0.174564 & 9.940612 & 1.68 \mathrm { E } - 06 \
\hline x _ { 2 } \text { (neighborhood) } & 49.12456 & 7.655776 & 6.416667 & 7.67 \mathrm { E } - 05 \
\hline
\end{array}$$ For what annual income will a suburban household and a rural household have the same predicted weekly grocery spending?

Quizplus · Accepted Answer

The coefficient for the neighborhood variable is positive, indicating that, all else being equal, rural households have a higher predicted weekly grocery spending than suburban households. This difference is constant regardless of income, so there is no income level at which the predicted spending for both types of households will be the same.

Abby Kratz, a Market Specialist at the Market Research Firm