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23 September, 06:20

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).

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  1. 23 September, 09:16
    0
    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)
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