Q: Using the regression equation from the previous question and the means $$\bar{x} = 3.2$$, $$\bar{y} = 2.8$$, what is the intercept ($$b_0$$)?

$$b_0 = 2.8 - 1.022$$ \times 3.2 = -0.47$$

Q: Using the regression equation from the previous question, what is the intercept ($$b_0$$)?

$$b_0 = 2$$,098.68 - 4.13 \times 388.24 = 2,098.68 - 1,603.46 = 495.22$$

Q: Using the regression equation $$\hat{y} = 495.22 + 4.13x$$, what is the predicted value of $$y$$ when $$x = 350$$?

$$\hat{y} = 495.22 + 4.13 \times 350 = 1,940.72$$

Question 1

A small town has a mean new home selling price of $$435,000 with a population standard deviation of 25$$,000. What is the probability that a randomly selected new home sells for more than $510,000? (Assume normality.)

Accepted Answer

$$P(Z \u003e 3) = 0.0013$$

Question 2

Given the same town with mean home price $$435,000 and standard deviation 25$$,000, what is the probability that a randomly selected home sells between $$385,000 and 410$$,000? (Assume normality.)

Accepted Answer

$$P(-2 \u003c Z \u003c -1) = 0.1359$$

Question 3

Given the following regression summary statistics: $$SS_{xy} = 66.233$$, $$SS_{xx} = 64.817$$, $$\sum x = 48$$, $$\sum y = 42$$, $$n = 15$$, what is the slope ($$b_1) of $$the regression equation?

Accepted Answer

$$b_1$$ = \frac{66.233}{64.817} = 1.022$$

Question 4

Using the regression equation from the previous question and the means $$\bar{x} = 3.2$$, $$\bar{y} = 2.8$$, what is the intercept ($$b_0$$)?

Accepted Answer

$$b_0 = 2.8 - 1.022$$ 	imes 3.2 = -0.47$$

Question 5

Given $$SSE = 106$$ and $$SST = 370$$, what is the coefficient of determination $$r^2$$?

Accepted Answer

$$r^2 = 1$$ - \frac{106}{370} = 0.71$$

Question 6

Given $$SSE = 240$$ and $$SSR = 915$$, what is the coefficient of determination $$r^2$$?

Accepted Answer

$$r^2$$ = \frac{SSR}{SSR + SSE} = \frac{915}{915 + 240} = 0.79$$

Question 7

In an ANOVA table for a regression with $$n = 50$$ observations, $$1$$ dependent variable, and $$5$$ independent variables, the residual sum of squares is $$42.05$$ and the total sum of squares is $$100.50. $$What is the $$r^2$$ value (rounded to two decimals)?

Accepted Answer

$$r^2 = 1$$ - \frac{42.05}{100.50} = 0.58$$

Question 8

Given $$SS_{xy} = 915.00$$, $$SS_{xx} = 221.55$$, $$n = 34$$, $$\bar{x} = 388.24$$, $$\bar{y} = 2,098.68$$, $$SSE = 37,178$$, and $$SST = 52,894$$, what is the slope ($$b_1) of $$the regression equation?

Accepted Answer

$$b_1$$ = \frac{915.00}{221.55} = 4.13$$

Question 9

Using the regression equation from the previous question, what is the intercept ($$b_0$$)?

Accepted Answer

$$b_0 = 2$$,098.68 - 4.13 	imes 388.24 = 2,098.68 - 1,603.46 = 495.22$$

Question 10

Given $$SSE = 37,178$$ and $$SST = 52,894$$, what is the coefficient of determination $$r^2$$ for the regression model?

Accepted Answer

$$r^2 = 1$$ - \frac{37,178}{52,894} = 0.30$$

Question 11

Using the regression equation $$\hat{y} = 495.22 + 4.13x$$, what is the predicted value of $$y$$ when $$x = 350$$?

Accepted Answer

$$\hat{y} = 495.22 + 4.13 	imes 350 = 1,940.72$$

Question 12

In a regression ANOVA table, if the regression sum of squares (SSR) is $$15,716$$ and the residual sum of squares (SSE) is $$37,178$$, what is the total sum of squares (SST)?

Accepted Answer

$$SST = SSR + SSE = 15,716 + 37,178 = 52,894$$

Question 13

A regression model with $$n = 34$$ and $$1$$ independent variable has $$SSE = 37,178. $$What are the degrees of freedom for the residuals?

Accepted Answer

$$df_{residual} = n - 2 = 32$$

Question 14

In a regression with $$n = 50$$ and $$5$$ independent variables, what is the degrees of freedom for the regression?

Accepted Answer

$$df_{regression} = 5$$

Question 15

If the mean square for regression (MSR) is $$15,716$$ and the mean square for error (MSE) is $$1,162.44$$, what is the $$F$$ statistic for the regression?

Accepted Answer

$$F = \frac{MSR}{MSE} = \frac{15,716}{1,162.44} = 13.52$$

Question 16

A researcher wants to predict the selling price of a home using square footage. The regression equation is $$\hat{y} = 50,000 + 200x$$, where $$x is $$the square footage. What is the predicted price for a 2,000 square foot home?

Accepted Answer

$$\hat{y} = 50,000 + 200 	imes 2,000 = 450,000$$

Question 17

Which of the following best describes the interpretation of the coefficient of determination ($$r^2) in $$regression analysis?

Accepted Answer

$$r^2$$ represents the proportion of the variance in the dependent variable explained by the independent variable(s).

Question 18

If a regression model has $$r^2 = 0.71$, what does this imply about the model's explanatory power?

Accepted Answer

71% of the variation in the dependent variable is explained by the independent variable(s).

Question 19

A real estate analyst uses regression to predict home prices. The regression output shows $$F = 13.52$$ with $$p \u003c 0.01. $$What does this indicate?

Accepted Answer

The regression model is statistically significant at the 1% level.

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