# Regression Analysis: Implementation and Interpretation

I. Simple Regression to Estimate Parameters.

(A) Simple regression model with sales revenue as the dependent Y-variable and R&D expenditures

independent X-variable.

(B) Simple regression model with profits as the dependent Y-variable and R&D expenditures

independent X-variable.

1. Submit printout of excel regression computation.

2. Write out linear equation with the estimated parameters.

3. Interpret the meaning of the coefficient, i.e. explain the impact of a one unit

change in the coefficient (parameter) value on the predicted (dependent) variable.

4. Use the estimated equation to calculate a new predicted value of the dependent

variable, i.e. make a forecast.

5. Explain the meaning of R square.

6. Explain the meaning of the F test of significance.

II. Multiple Regression to Estimate Parameters.

Demand Function Electronic Data Processing, Inc.

Y P SE AD

Unit Sales Price Selling Ex Expenses

100 3800 14250 13500

110 3700 15000 15000

130 3500 17000 17250

170 3200 18750 22500

140 3900 21750 18000

210 2500 23250 16500

230 2300 22500 24000

250 2100 24000 15000

200 3400 21000 24750

220 2500 24750 19500

240 2400 25500 24750

200 3300 29250 12000

1. Submit printout of excel computation.

2. Write out linear equation with the estimated parameters.

3. Interpret the meaning of the coefficients, i.e. explain the impact of a one unit

change in each coefficient (parameter) value on the predicted (dependent) variable.

4. Using the t-test of significance, indicate which variables are statistically significant enough to

use to forecast.

5. Use the estimated equation to calculate a new predicted value of the dependent

variable, i.e. make a forecast.

6. Explain the meaning of R square.

7. Explain the meaning of the F test of significance.

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#### Solution Preview

Procedure for Regression Analysis in Excel

1. Enter data in an excel sheet giving variable names in the first row

2. Tools > Data Analysis > Regression > OK

3. Click on Input Y Range (Select the dependent variable range including the variable name)

4. Click on Input X Range (Select the independent variables range including the variable names)

5. Click the check box against Labels in the First Row

6. Click OK

7. We get the output as a new sheet in Excel

I. Simple Regression to Estimate Parameters

Problem A

1. Adopt the procedure described above to produce the regression output (See sheet Reg1 of the attached excel file Simple Reg 272749)

2. Y = 1364.797 + 16.889 X

(582.409) (1.093)

NB. Figures in the parenthesis provide the standard error of the estimated coefficients

Y = Sales Revenue; X = R & D Expenditure

3. Discussion: The regression coefficient provides the rate of change in the value of the dependent variable with respect to a change in the values of the independent variable. For example if the regression coefficient is +1, it means one unit increase/decrease in the independent variable produces one unit increase/decrese in the dependent variable. If regression coefficient is -1, it means one unit increase/decrease in the independent variable produces one unit decrease/increase in the dependent variable. Thus if the regression coefficient is positive then one unit increase/decrease in the value of the coefficient (parameter) produces X unit increase / decrease in the value of the dependent variable .On the other hand if the regression coefficient is negative then one unit increase/decrease in the value of the coefficient produces X units decrease /increase in the value of the dependent variable

Present Problem: In the present problem regression coefficient is + 16.889, hence it means that one dollar increase in the R&D expenditure will produce 16.889 dollars increase in Sales Revenue on the average.

Also, one unit increase/decrease in the value of the coefficient produces an increase/ decrease in the in Sales Revenue equivalent to the value of R&D expenditure.

4. The estimated equation can be used ...

#### Solution Summary

This solution gives an illustration of how, simple and multiple regression analysis can be implemented (using the analysis tool pack of M.S. Excel) and interpret it properly. The general procedure for implementing the analysis is provided. Two simple regression analysis problems and one multiple regression analysis problem are given as examples. The regression equations obtained are used for predicting the value of the dependent variable for the given values of the independent variables.

The calculations are provided as Excel files so that students can easily understand how these problems are worked out.

The meaning of the various regression outputs such as regression coefficients, t values, R square, F value and p values are provided as general explanation and illustrated using the examples.