4 Correlation and Regression

Chapter 4 Review Exercises

237

section 4.1

Square footage and home price in Broward County, Florida. The following table contains the square footage and price of a sample of homes in Broward County, Florida. Use this data for Exercises 1–17.

Home	Square feet	Price
1	1500	$156,250
2	2000	$225,000
3	2000	$325,000
4	2500	$412,500
5	2500	$275,000
6	3000	$525,000
7	3000	$625,000
8	3500	$756,250

Question 4.294

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1. Construct a scatterplot of price versus square feet.

4.99.1

Question 4.295

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2. Refer to your scatterplot from Exercise 1. Characterize the relationship as positive, negative, or not apparent.

Question 4.296

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3. Write a sentence that describes the behavior of the price as the square footage increases.

4.99.3

As the number of square feet increases, the price also tends to increase.

Question 4.297

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4. Calculate the value of the correlation coefficient between price and square feet.

Question 4.298

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5. Interpret the value for .

4.99.5

This value of is very close to the maximum value . We would therefore say that price and square feet are positively correlated. As square feet increases, price also tends to increase.

section 4.2

Question 4.299

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6. Calculate the regression coefficients and , and write the regression equation.

Question 4.300

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7. State the regression equation in words.

4.99.7

The predicted price of a house is 300.0 times the number of square feet minus $337,500.

Question 4.301

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8. Interpret the value of the slope .

Question 4.302

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9. Interpret the value of the intercept .

4.99.9

,500 means that the predicted price for a home with square feet is –$337,500.

Question 4.303

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10. Use the regression equation to predict the price for a home with 3500 square feet.

Question 4.304

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11. Calculate and interpret the prediction error in Exercise 10.

4.99.11

$43,750. The actual observed price of house with 3500 square feet lies above the predicted price of a house with 3500 square feet.

Question 4.305

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12. Use the regression equation to predict the price for a home with 4500 square feet. State whether the prediction represents extrapolation.

section 4.3

Question 4.306

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13. Calculate SSE.

4.99.13

33,359,375,000

Question 4.307

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14. Calculate , the standard error of the estimate. What does this number mean?

Question 4.308

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15. Calculate SST, and then use SSE and SST to find SSR.

4.99.15

SST = 3.03359 × 10¹¹, SSR = 2.70000 × 10¹¹

Question 4.309

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16. Calculate , the coefficient of determination. Comment on how useful square footage is for predicting price.

Question 4.310

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17. Use to calculate the correlation coefficient. Comment on the relationship between square footage and home price.

4.99.17

0.9434. This value of is very close to the maximum value . We would therefore say that price and square feet are positively correlated. As square feet increases, price also tends to increase.