1. Linear Regression Using Excel

2. Example
All of this can also be done automatically in Excel.
Go to Tools
Data Analysis
Regression
Choose the y data, then the x data.

3. Example

4. Example SSR/SST = 41402/42892 = 1 – SSE/SST = 1490/42892 SSR SSE SST

5. Multiple Linear Regression

6. Example
Example
Develop a model for estimating heating oil used for a single family home in the month of January based on average temperature and amount of insulation in inches.
(oF)
(in.)

7. Example
Start by plotting the data to take a look.
What size of R2 values will we expect for each of these variables alone?

8. Example
Start with Simple Linear Regressions for each
Excel output

9. Start with Simple Linear Regressions for each
Example
Start with Simple Linear Regressions for each
Temperature
R2 = 0.756
Insulation
R2 = 0.216

10. Multiple Linear Regression In general
Example
Multiple Linear Regression
In general
independent (explanatory) variables
dependent (response) variable
residual
In this problem, fit

11. Excel output Example Multiple Linear Regression
For each degree increase in temperature, the estimated average amount of heating oil used is decreased by gallons, holding insulation constant.
For each increase in one inch of insulation, the estimated average use of heating oil is decreased by gallons, holding temperature constant.

12. Example R2
never decreases when a new X variable is added to the model
a disadvantage when comparing models
Multiple Linear Regression
Excel output
Adjusted R2
reflects the number of x variables and sample size
penalizes excessive use of independent variables
useful in comparing different models
smaller than r2 = a
96.56% of total variation explained by temperature and amount of insulation
95.99% of the total variation explained by temperature and insulation after adjusting for # of variables and sample size

13. Example
Example
Predict the amount of heating oil used for a home if the average temperature is 300 and the insulation is six inches.