Explore BrainMass
Share

Explore BrainMass

    Linear regression - Confidence interval, prediction interval

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Hanna Properties specializes in custom-home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand.

    x= 26,27,33,29,29,34,30,40,22
    y= 290,305,325,327,356,411,488,554,246
    Now we want to build the linear regression model,

    *With the information provided above please answer the followin questions:
    1. Do the data suggest that size is useful as a predictor if price for custom homes in the Equestrain Estates? Perform the required hypothesis at the 0.01 level of significance.

    2. a. Find a 99% confidence interval for the slope of the population regression line that relates price to size for custom homes in the Equestraion Estates.

    b. Interpret your answer to part (a).

    3. a. Determine a point estimate for the mean price of all 2800-sq-ft Equestrain Estates home.

    b. Find 99% confidence interval for the mean price of all 2800-sq-ft Equestrain Estate.

    c. Find the predicted price of a 2800-sq-ft Equestrain Estate home.

    d. Determine a 99% prediction interval for the price of a 2800-sq-ft Equestrain Estate home.

    4. At the 0.5% significance level, do the data provide sufficiant evidence to conclude that, for custom homes in the Equestrain Estates, size and price are positively linearly correlated?

    © BrainMass Inc. brainmass.com October 9, 2019, 6:35 pm ad1c9bdddf
    https://brainmass.com/statistics/linear-regression/linear-regression-confidence-interval-prediction-interval-92131

    Solution Preview

    See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

    Hanna Properties specializes in custom-home resales in the Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand
    X Y X^2
    26 290 676
    27 305 729
    33 325 1089
    29 327 841
    29 356 841
    34 411 1156
    30 488 900
    40 554 1600
    22 246 484
    30 366.8888889 Average
    8316 Total
    Run regression on the data. Go to tools, data analysis and regression.
    The regression output is below

    SUMMARY OUTPUT

    Regression Statistics
    Multiple R 0.828731691
    R Square 0.686796216
    Adjusted R ...

    Solution Summary

    A very good post to learn the concepts of linear regression. It touches upon various concepts involved with regression while solving the case of Equestraion Estates.

    $2.19