Question

It is determined that the relationship between the number of rooms in a house and the number of kilowatt hours of electricity consumed is as follows: Coefficients Standard Error t Stat P-value Intercept 1.333333333 1.05586364 1.262789 0.242227 Rooms 0.666666667 0.11160826 5.973274 0.000333 22. If the value of the coefficient of determination is .81, this means that: A. The value of r = .9 B. The value of r = -.9. C. We cannot determine the value of r for certain because both (.9)2 and (-.9)2 are equal to .81. D. 81% of the variation in Y is not explained. 23. Which of the following statements is true about the variable “rooms”: A. A good predictor of the value of kilowatt hours. B. A poor predictor of the value of kilowatt hours. C. Not significant D. For each additional room, the amount of electricity used increases by 1.33333333. 24. Which of the following statements is not true about the intercept: A. It is an estimate of the amount of kilowatt hours not explained by rooms. B. For each additional one unit increase in rooms, kilowatt hours increases by 1.33333333. C. When the number of rooms is 0, the kilowatt hours used is 1.33333333. D. It is the point at which the regression line crosses the y axis.

Answer 1

Solution:

We are given following regression output:

	Coefficients	Standard Error	t Stat	P-value
Intercept	1.333333333	1.05586364	1.262789	0.242227
Rooms	0.666666667	0.11160826	5.973274	0.000333

Question 22. If the value of the coefficient of determination is .81, this means that:

Since r² = 0.81 , then r = square root( 0.81) =0.9 and since slope = 0.6666666667 which is positive, thus r is also positive.

Thus correct answer is: A. The value of r = .9

Question 23. Which of the following statements is true about the variable “rooms”:

Since P-value for significance of slope is 0.000333 < 0.05 level of significant, hence variable rooms is significant.

Thus correct answer is: A. A good predictor of the value of kilowatt hours.

Question 24. Which of the following statements is not true about the intercept:

Intercept is a constant term in regression line which is the value of kilowatt hours when number of rooms is 0.

It it is point on y axis and when number of rooms is 0 , it is the an estimate of the amount of kilowatt hours not explained by rooms.

Thus options A, C and D are true.

Since it says for each additional one unit increase in rooms, kilowatt hours increases by 1.33333333.

But actually for each additional one unit increase in rooms, kilowatt hours increases by slope amount 0.666666667

Thus correct answer is: Option B is not true.

B. For each additional one unit increase in rooms, kilowatt hours increases by 1.33333333.