A test is conducted in 22 cities to see if giving away free transit system maps will increase the number of bus riders. In a regression analysis, the dependent variable Y is the increase in bus riders (in thousands of persons) from the start of the test until its conclusion. The independent variables are X₁ = the number (in thousands) of free maps distributed and a binary variable X₂ = 1 if the city has free downtown parking, 0 otherwise. The estimated regression equation is $\hat { Y } = 1.32 + 0.0345 X _ { 1 } - 1.45 X _ { 2 }$ . In city 3, the observed Y value is 7.3, X₁ = 140, and X₂ = 0. The residual for city 3 (in thousands) is: A)6.15. B)1.15. C)4.83. D)1.57.

Question

Quizplus · Accepted Answer

The residual is calculated as the observed value minus the predicted value. The predicted value for city 3 can be calculated using the regression equation $\hat { Y } = 1.32 + 0.0345(140) - 1.45(0)$. This simplifies to $\hat { Y } = 1.32 + 4.83 - 0 = 6.15$. The observed value is 7.3, so the residual is $7.3 - 6.15 = 1.15$.

A Test Is Conducted in 22 Cities to See If Y^=1.32+0.0345X1−1.45X2\hat { Y } = 1.32 + 0.0345 X _ { 1 } - 1.45 X _ { 2 }Y^=1.32+0.0345X1​−1.45X2​

A Test Is Conducted in 22 Cities to See If $\hat { Y } = 1.32 + 0.0345 X _ { 1 } - 1.45 X _ { 2 }$