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    Test the significance of the slope and y-intercept

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    Information:
    A real estate agency collects data concerning y = the sales price of a house (in thousands of dollars), and x = the home size (in hundreds of square feet). The MINITAB output of a simple linear regression analysis of the data set for this case is given in table (below).

    MINITAB Output of a Simple Linear Regression Analysis of the Real Estate Sales Price Data

    The regression equation is
    SPrice = 48.0 + 5.70 HomeSize

    Predictor Coef SE Coef T P
    Constant 48.02 14.41 3.33 0.010
    HomeSize 5.7003 0.7457 7.64 0.000

    S = 10.5880 R-Sq = 88.0% R-Sq(adj) = 86.5%

    Analysis of Variance
    Source DF SS MS F P
    Regression 1 6550.7 6550.7 58.43 0.000
    Residual Error 8 896.8 112.1
    -------- ---------- ---------
    Total 9 7447.5

    Values of Predictors for New Observations

    New Obs HomeSize
    1 20.0

    Predicted Values for New Observations

    New Obs Fit SE Fit 95% CI 95% PI
    1 162.03 3.47 (154.04, 170.02) (136.34, 187.72)

    Real Estate Sales Price Data
    Sales Price (y) Home Size (x)
    180 23
    98.1 11
    173.1 20
    136.5 17
    141 15
    165.9 21
    193.5 24
    127.8 13
    163.5 19
    172.5 25

    (a) Find the least squares point estimates b0 and b1 of β0 and β1 on the output and report their values.(Round b0 to 2 decimal places and b1 to 4 decimal places.)

    b0 ______
    b1 ______

    (b) Find SSE and s on the computer output and report their values. (Round SSE to 1 decimal place and s to 3 decimal places.)

    SSE _______
    s _______

    (c) Find sb1 and the t statistic for testing the significance of the slope on the output and report their values. Show (within rounding) how t has been calculated by using b1 and sb1 from the computer output. (Round sb1 to 4 decimal places and t to 2 decimal places.)

    sb1 _______
    t _______

    (d) Using the t statistic and appropriate critical value, test H0: β1 = 0 versus Ha: β1 ≠ 0 by setting α equal to .05. Is the slope (regression relationship) significant at the .05 level?

    (Choose one) Reject / Do Not Reject not reject

    H0. The slope is (Choose one) Not Significant / Significant at the .05 level.

    (e Using the t statistic and appropriate critical value, test H0: β1 = 0 versus Ha: β1 ≠ 0 by setting α equal to .01. Is the slope (regression relationship) significant at the .01 level?

    (Choose one) Do not reject / Reject

    H0. The slope is (Choose one) Not Significant / Significant at the .01 level.

    (f) Find the p-value for testing H0: β1 = 0 versus Ha: β1 ≠ 0 on the output and report its value. Using the p-value, determine whether we can reject H0 by setting α equal to .10, .05, .01, and .001. How much evidence is there that the slope (regression relationship) is significant? (Round your answer to 3 decimal places.)

    p- value = _________ reject at (Choose one )
    none
    all α.
    10 and .05

    (g) Calculate the 95 percent confidence interval for β1 using numbers on the output. (Round your answers to 4 decimal places.)

    [ ______ , ______ ]

    (h) Calculate the 99 percent confidence interval for β1 using numbers on the output. (Round your answers to 3 decimal places.)

    [ ______ , _______ ]

    (i) Find sbo and the t statistic for testing the significance of the y intercept on the output and report their values. Show how t has been calculated by using b0 and sb0 from the computer output. (Round your answers to 2 decimal places.)

    sb0 ___________________
    t ___________________

    (j) Find the p-value for testing H0: β0 = 0 versus Ha: β0 ≠ 0. Using the p-value, determine whether we can reject H0 by setting α equal to .10, .05, .01, and .001. What do you conclude about the significance of the y intercept? (Round your answer to 3 decimal places.)

    p-value = __________
    reject at (Choose one)
    0.10 and 0.05, but not at 0.01 or 0.001
    0.10 and but not at 0.05, 0.01 or 0.001
    0.10, 0.05, and 0.01 but not at 0.001
    None

    (k) Using the appropriate data set and s from the computer output, hand calculate SSxx, sbo, and sb1. (Round your answers for SSxx to 1 decimal place and sb1 to 4 decimal places and sb0 to 2 decimal places.)

    SSxx _________________
    sb1 _________________
    sbo _________________

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    https://brainmass.com/statistics/regression-model-validation/test-the-significance-of-the-slope-and-y-intercept-562256

    Solution Summary

    The solution contains detailed regression analysis performed on the given data and answers to the given questions.

    $2.19

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