Q: Given the regression equation $$y = 495.25x + 1,946.75$$, what is the predicted value of $$y$$ when $$x = 390$$?

$$y = 495.25 \times 390 + 1,946.75 = 195,103.75$$

Question 1

A small town has a mean selling price of new homes of $$\435$$,000$$ with a population standard deviation of $$\$$25,000. $$What is the $$z-$$score for a home sold at $$\510$$,000$?

Accepted Answer

$$z = \frac{510,000 - 435,000}{25,000} = 3$$

Question 2

Given the same town, what is the probability that a randomly selected home sells for more than $$\510$$,000$? Use the standard normal distribution.

Accepted Answer

0.135%

Question 3

What is the $$z-$$score for a home sold at $$\420$$,000$ in the same town?

Accepted Answer

$$z = \frac{420,000 - 435,000}{25,000} = -0.6$$

Question 4

What is the probability that the selling price was between $$\420$$,000$$ and $$\$$455,000$$?

Accepted Answer

45.2%

Question 5

Given the regression equation $$y = 495.25x + 1,946.75$$, what is the predicted value of $$y$$ when $$x = 390$$?

Accepted Answer

$$y = 495.25 	imes 390 + 1,946.75 = 195,103.75$$

Question 6

If the sum of squares for regression (SSR) is $$58.45$$ and the sum of squares for error (SSE) is $$1.16$$, what is the total sum of squares (SST)?

Accepted Answer

$$SST = SSR + SSE = 58.45 + 1.16 = 59.61$$

Question 7

What is the coefficient of determination ($$R^2) if$$ $$SSR = 58.45$$ and $$SST = 59.61$$?

Accepted Answer

$$R^2$$ = \frac{SSR}{SST} = \frac{58.45}{59.61} = 0.98$$

Question 8

In an ANOVA table, if the mean square for regression (MSR) is $$58.45$$ and the mean square for error (MSE) is $$1.16$$, what is the $$F-$$statistic?

Accepted Answer

$$F = \frac{MSR}{MSE} = \frac{58.45}{1.16} = 50.38$$

Question 9

If the regression equation is $$y = 495.25x + 1,946.75$$, what is the value of $$x$$ when $$y = 15,560$$?

Accepted Answer

$$x = \frac{15,560 - 1,946.75}{495.25} = 27.5$$

Question 10

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

Accepted Answer

$$R^2$$ represents the proportion of variance in the dependent variable explained by the independent variable.

Question 11

A researcher wants to test if the regression model is significant. Which value from the ANOVA table should be compared to a critical value from the $$F-$$distribution?

Accepted Answer

The $$F-$$statistic

Question 12

If the probability that a home sells for more than $$\510$$,000$$ is 0.135$$\%$$, what is the probability that a home sells for less than $$\$$510,000$$?

Accepted Answer

99.865%

Question 13

Which of the following is NOT a correct interpretation of a $$z-$$score?

Accepted Answer

A $$z-$$score is always positive.

Question 14

If the sum of squares for error (SSE) is very small compared to the sum of squares for regression (SSR), what does this indicate about the regression model?

Accepted Answer

The model explains most of the variability in the data.

Step-by-Step Guidance for Statistics Worksheet: Regression, Probability, and ANOVA

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