Regression in EXCELPumpkin experiment

Regression StatisticsMultiple R 0.968R Square 0.937Adjusted R Square 0.934Standard Error 3.260Observations 23.000

ANOVAdf SS MS F Significance F

Regression 1 3334.239 3334.239 313.650 0.000Residual 21 223.239 10.630Total 22 3557.478

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 33.293 1.372 24.272 0.000 30.440 36.145Circumference 0.011 0.001 17.710 0.000 0.010 0.013

r2

SSE

SSTb1b0

Prediction Watch Outs Consider only the relevant range

of the explanatory variable (x) Interpolation is valid Extrapolation is not!!!

Linear Regression in ExcelMethod 1

When all you need is the slope and intercept of a best fit line, you can use Excel functions (SLOPE and INTERCEPT) to determine these values. You can also use RSQ to find the coefficient of determination (R2)

Example #1

Using Excel’s Functions to find the slope, intercept, and

coefficient of determination

Linear Regression in ExcelMethod 2

Performing a linear regression in Excel is very easy. Once the data have been graphed, regression can be done very simply. Just because it is easy, does not mean that a linear regression always makes sense. Graph the data first and always inspect the “quality” of the fit.

Linear Regression in ExcelMethod 2

When regression is done with the trend line feature of Excel, the fitted curve is automatically added to the graph.

Linear Regression in ExcelMethod 2

The process of performing a linear regression for a slope and intercept requires the computation of various sums using both the independent (x) values and dependant (y) values in the data set being analyzed.

Linear Regression in ExcelMethod 2 You can calculate the slope b1 and

intercept b0 with formula’s, but Excel will do this for you

When trying to find the best fit, always start with a linear fit (unless it is obvious that won’t work), then try exponential and polynomial fits if you think you can get a better fit.

Example #2

Using Excel’s Trendline feature find the equation for a

model that fits the data

Linear Regression in ExcelMethod 3 There is an add-in under tools

(regression) that can provide you all the details resulting from a linear regression.

It is easy to use, but interpreting the results requires some understanding of regression terminology

Example #3

Using Excel’s Regression Analysis Tool

Solving Equations

You can use Excel to solve a single equation. Like most things in Excel you can do this in many different ways

Graphical solution (find the roots of an equation)

Trial and guess Excel features…solver and goal seek

Example #1

Using Graphical means to find equation solution

Example #2

Using Goal Seek to find equation solution

Example #3

Using Solver to find solutions