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 monthly 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.

Coefficients Standard Error t Statistic p‐value Intercept 39.14942 22.30182 1.755436 0.109712 x 1.792312 0.407507 4.398234 0.001339
Source df SS MS F Se = 29.51443
Regression 1 16850.99 16850.99 19.34446 r2 = 0.682478
Residual 9 7839.915 871.1017
Total 10 24690.91
For a rural household with $90,000 annual income, Abby's model predicts weekly grocery expenditure of:_________.
a) $150.35
b) $50.35
c) $1,959.29
d) $128.65
e) $1286.50

Answer 1

d) $128.65

Explanation:

The table format from the question can be properly expressed as :

Coefficients Standard Error t Statistic p value

Intercept 39.14942 22.30182 1.755436 0.109712

x 1.792312 0.407507 4.398234 0.001339

Source df SS MS F
`S_e` = 29.51443

Regression 1 16850.99 16850.99 19.34446
`r^2` = 0.682478

Residual 9 7839.915 871.1017

Total 10 24690.91

For a rural household with $90,000 annual income, Abby's model predicts weekly grocery expenditure of:_________.

The estimated regression equation is as follows:

Expenditure (y) = 39.15 + 1.79 x

For a rural household with $90,000 annual income; the independent variables will assume the following values

x = 50

Thus; the estimated groceries expenditure is computed from the above regression equation by replacing the values of the independent variables;

This can be expressed as:

y = 39.15 + 1.79 (50)

y = 39.15 + 89.5

y = $128.65