Question

Fifteen houses rented recently in a certain county provided the data: size of the house x (in sq.ft.) and the monthly renty (in thousands of dollars). The sample data are summarized by the following information: n = 15. Ex = 16,560, y = 21.685, Exy = 28,474.85. Ex2 = 22,557,866, y2 = 36.93, 6505 x 52,400 The following sums were also computed: SSxy=4,534.61, SSxx = 4,275,626, SSyy = 5.5807 1. Which of the following is the slope of the least squares regression line? [Select) 2. The y-intercept of the least squares regression line is: [Select) 3. Which of the following is the least squares regression line? (Select] 4. The interpretation of the meaning of the slope of the least squares regression line in the context of the problem is that: For each unit increase in x (additional size of 1 square feet), [Select) 5. Suppose a rented house is selected at random from the county whose size is 700 sq. ft. Using the regression equation, which of the following predicts its monthly rent? (Select]

Answer 1

1)

Slope = SS_​​​xy /SS_{​​​​​xx} = 4534.61/4275626 = 0.00106

2)

y - intercept = = 0.2748

Σ» T SS ry SS s n TT n

3)

The least squares regression line is

$\hat{y}$ = 0.00106x + 0.2748

4)

The average monthly rent increases by about 0.00106 units (about $1.06)

5)

The predicted monthly rent = 0.00106*700 + 0.2748

= $1.017

I.e. $1017