The following data on average daily hotel room rate and amount spent on entertainment (The Wall Street Journal, August 18, 2011) lead to the estimated regression equation ŷ = 17.49 + 1.0334x. For these data SSE = 1541.4.

City Room Rate ($) Entertainment ($)

Boston 148 161

Denver 96 105

Na. shville 91 101

New Orleans 110 142

Phoenix 90 100

San Diego 102 120

San Francisco 136 167

San Jose 90 140

Tampa 82 98

(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 haye a daily room rate of $89 (to 2 decimals).

(c) The average room rata in Chicago is $128. Develop a 95% prediction interval for the amount spent on entertainment in Chicago (to 2 decimals).

a. Predicted Amount = $109.46

b. Confidence Interval = (94.84,124.08)

c. Interval = (110.6883,188.8517)

Step-by-step explanation:

Given

ŷ = 17.49 + 1.0334x.

SSE = 1541.4

a.

ŷ = 17.49 + 1.0334 (89)

ŷ = 109.4626

ŷ = 109.46 - - - Approximated

Predicted Amount = $109.46

b.

ŷ = 17.49 + 1.0334 (89)

ŷ = 109.4626

ŷ = 109.46

First we calculate the standard deviation

variance = SSE / (n-2)

v = 1541.4 / (9-2)

v = 1541.4/7

v = 220.2

s = √v

s = √220.2

s = 14.839

Then we calculate mean (x) and ∑ (x - (mean (x)) ²

X - - - Y - - Mean (x) - - - ∑ (x - (mean (x)) ²

148 - - 161 - - 43- - 1849

96 || 105|| - 9 || 81

91 ||101 || - 14 || 196

110 || 142 || 5 || 25

90 || 100 || - 15 || 225

102 || ||120 ||-3|| 9

136 || 167 ||31 ||961

90 || 140 ||-15 ||225

82 || 98 ||-23 || 529

Sum 945 || 1134|| 0 ||4100

Mean (x) = 945/9 = 105

∑ (x - (mean (x)) ² = 4100

α = 1 - 95% = 5%

α/2 = 2.5% = 0.025

tα, df = n - 2 = t0.025,7 = 2.365

Confidence interval = 109.46 ± 2.365 * 14.839 √ ((1/9) + (89-105) ²/4100

Confidence Interval = (109.46 ± 14.62)

Confidence Interval = (94.84,124.08)

c.

ŷ = 17.49 + 1.0334 (128)

ŷ = 149.7652

ŷ = 149.77

Interval = 149.77 ± 2.365 * 14.839 √ ((1/9) + (128-105) ²/4100

Interval = 149.77 ± 39.0817

Interval = (110.6883,188.8517)