A county real estate appraiser wants to develop a statistica

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model:

Yhat = ₀ + ₁X

where Y = appraised value of the house (in $thousands) and X = number of rooms in the home.   Using data collected for a sample of n = 74 houses in East Meadow, the following results were obtained:

     Yhat = 74.80 + 19. 70X

     Range of the x-values: 5 - 11

     Range of the y-values: 160 - 300

Give a practical interpretation of the estimate of the slope of the least squares regression line.

A)For a house with 0 rooms, we estimate the appraised value to be $74,800.

B)For each additional room in the house, we estimate the appraised value to increase $74,800.

C)For each additional dollar of appraised value, we estimate the number of rooms in the house to increase by 19.70 rooms.

D)For each additional room in the house, we estimate the appraised value to increase $ 19, 700.

Solution

Slope of least square regression line tells that how much value of Y increase (if slope is positive) or decrese (if slope is negative) with each unit increase of X.

In the given regression equation slope is 19.70 that is $19,700. So it tell us that for each additional room in the house, we estimate the appraised value to increase $ 19, 700.

Hence, option D is correct.