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    Simple and Multiple Regression

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    This assignment introduces you to applications of simple and multiple regression. You will apply these models for predicting and forecasting and, determining the strength of the relationship between a variable y and a number of variables X1, ..., Xp.

    Skill- Building Exercises:

    ? 1. For the Home Market Value data, use formulas (6.2) and (6.3) on a spreadsheet to calculate the least-squares regression coefficients.

    ? 2. For the Colleges and Universities data, plot scatter charts for each variable individually against the graduation rate and add linear trendlines, finding both the equation and R2 values.

    ? 3. Use the regression tools to find simple linear regression models for each independent variable for the Colleges and Universities data.

    ? 4. Use the INTERCEPT and SLOPE functions in Excel to develop regression models for each of the independent variables in the Colleges and Universities example.

    Number and identify each part of the answer concerning the college and university: ie, 2, 3 or 4

    Problems and Applications:

    12. The Excel file Concert Sales provides data on sales dollars and the number of radio and TV and newspaper ads promoting the concerts for a group of cities. Develop simple linear regression models for predicting sales as a function of the number of each type of ad. Compare these results to a multiple linear regression model using both independent variables. Examine the residuals of the best model for regression assumptions and possible outliers.

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    https://brainmass.com/statistics/regression-analysis/simple-and-multiple-regression-344521

    Attachments

    Solution Preview

    See attached files.

    The output is in the Excel file and below:

    a) House Age

    b1 = 1570.434183

    b2 = 45217.76115

    The regression equation is: y = 1570.4x + 45218

    b) Square Feet

    b1 = 35.03637258

    b2 = 32673.2199

    The regression equation is: y = 35.036x + 32673

    ? 2. For the Colleges and Universities data, plot scatter charts for each variable individually against the graduation rate and add linear trendlines, finding both the equation and R2 values.

    This has been done in the Excel file. The equation of the trendline and the R^2 value for each scatterplot is displayed in the chart.

    ? 3. Use the regression tools to find simple linear regression models for each independent variable for the Colleges and Universities data.

    The output is in the Excel file and below:

    (a) Median SAT

    Regression Statistics
    Multiple R 0.564146827
    R Square 0.318261642
    Adjusted R Square 0.303756571
    Standard Error 6.215134216
    Observations 49

    ANOVA
    df SS MS F Significance F
    Regression 1 847.5502382 847.5502382 21.94140465 2.42598E-05
    Residual 47 1815.510986 38.62789332
    Total 48 2663.061224

    Coefficients Standard Error t Stat P-value
    Intercept -1.438019781 18.10033983 -0.079447115 0.937014306
    Median SAT 0.067043608 0.014312818 4.68416531 2.42598E-05

    The regression equation is: y = 0.067x - 1.438

    (b) Acceptance Rate

    Regression Statistics
    Multiple R 0.55037751
    R Square 0.302915404
    Adjusted R Square 0.288083817
    Standard Error 6.284697658
    Observations 49

    ANOVA
    ...

    $2.19