Linear Regression Using Excel

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.

Example

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

Multiple Linear Regression

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.)

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

Example Start with Simple Linear Regressions for each Excel output

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

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

Excel output Example Multiple Linear Regression For each degree increase in temperature, the estimated average amount of heating oil used is decreased by 5.437 gallons, holding insulation constant. For each increase in one inch of insulation, the estimated average use of heating oil is decreased by 20.012 gallons, holding temperature constant.

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

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