Question

The regression equation below relates the scores students in an advanced statistics course received for homework completed and the subsequent midterm exam. Homework scores are based on assignments that preceded the exam. The maximum homework score a student could obtain was 500 and the maximum midterm score was 350. The regression line that was obtained is given byIf a student had a homework score of 420, the midterm score would be predicted to be (rounded to an integer):298.378.None of the answer choices is correct.336.An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree days, where a day's degree-days are the number of degrees its average temperature falls below 65 degrees F) over a 23-month period. By looking at the equation of the least-squares regression line (ŷ = 85 + 16x), you can see that the correlation between amount of gas used and degree-days isgreater than zero.less than zero.

Answer 1

The regression equation give for the first question is y=-84.4 + .91x

Answer:

Kindly check explanation

Explanation:

Given the regression equation y=-84.4 + .91x

Homework score (independent variable) = x

Midterm score (predicted variable) = y

If Homework score (x) = 420

y = - 84.4 + 0.91(420)

y = - 84.4 + 382.2

y = 297.8

= 298 ( nearest integer)

B.) Given the regression equation :

ŷ = 85 + 16x

The correlation between amount of gas and degree days is greater than 0, the Coefficient 16 represents the gradient, that is change in y per change in x. Since the value is positive, it depicts a positive correlation( greater than zero).