# Simple and Multiple Regression

[See attached files.]

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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#### 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

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