The following data on x = average daily hotel room rate and y = amount spent on

Question

The following data on x = average daily hotel room rate and y = amount spent on entertainment (The Waif Street Journal, August 18, 2011) lead to the estimated regression equation cap y = 17.49 + 1.0334x. For these data SSE = 1541.4. a. Predict the amount spent on entertainment for a particular city that has a daily room rate of $89 (to 2 decimals). b. Develop a 95% confidence interval for the mean amount spent on entertainment for all cities that have a daily room rate of $89 (to 2 decimals). c. The average room rate in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).

Explanation / Answer

Answer:

a). 109.47

b). 95% CI= (94.85, 124.08)

c). 95% PI = (110.69, 188.84)

Regression Analysis

r²

0.740

n

9

r

0.860

k

1

Std. Error

14.839

Dep. Var.

Entertainment

ANOVA table

Source

SS

df

MS

F

p-value

Regression

4,378.5778

1  

4,378.5778

19.88

.0029

Residual

1,541.4222

7  

220.2032

Total

5,920.0000

8  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=7)

p-value

95% lower

95% upper

Intercept

17.4915

24.8314

0.704

.5039

-41.2255

76.2084

Roomrate

1.0334

0.2318

4.459

.0029

0.4854

1.5814

Predicted values for: Entertainment

95% Confidence Intervals

95% Prediction Intervals

Roomrate

Predicted

lower

upper

lower

upper

Leverage

89

109.465

94.847

124.083

71.453

147.478

0.174

128

149.769

132.574

166.964

110.693

188.844

0.240

Regression Analysis

r²

0.740

n

9

r

0.860

k

1

Std. Error

14.839

Dep. Var.

Entertainment

ANOVA table

Source

SS

df

MS

F

p-value

Regression

4,378.5778

1  

4,378.5778

19.88

.0029

Residual

1,541.4222

7  

220.2032

Total

5,920.0000

8  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=7)

p-value

95% lower

95% upper

Intercept

17.4915

24.8314

0.704

.5039

-41.2255

76.2084

Roomrate

1.0334

0.2318

4.459

.0029

0.4854

1.5814

Predicted values for: Entertainment

95% Confidence Intervals

95% Prediction Intervals

Roomrate

Predicted

lower

upper

lower

upper

Leverage

89

109.465

94.847

124.083

71.453

147.478

0.174

128

149.769

132.574

166.964

110.693

188.844

0.240

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