In this unit we explore how the concept of linear regression is used to model data from a sample. We use MS Excel 2010 to generate a line of best fit, a linear equation that approximates the data values, and then we use the equation to predict other data values.

To complete this discussion, find a YouTube video that gives an example of how a linear equation line of best fit is determined from a data set using Microsoft Excel. Post the video and answer the following questions:

1) What does the data represent?

2) What is the independent variable (x-values)?

3) What is the dependent variable (y-values)?

4) What is the equation for the line of best fit that is determined using the Microsoft Excel Regression Analysis tool on the data?

5) Interpret the coefficients in this equation (the number in front of x, b1, and the constant, bo).

Notes on interpreting the coefficients:

• The intercept,b₀, is the value of y if the value ofxwere 0.
• The coefficient of the independent variable,b₁, is the amount by whichychanges if the value ofxis increased by1.

6) What is the value of R² ("R-squared" in Excel)? Interpret this.

          Notes on interpreting R²:

• If R²> 0.90, then the variablexis aVERYGOODpredictor of the variabley. Over 90% of the variance in the value of y can be explained by changes in the value ofx. This equation should be used to predict y-values from x-values.
• If R²is more than 0.70 but less than 0.90, then the variablexis an acceptable predictor of the variabley. Between 70% and 90% of the variance in the dependent variableycan be explained by changes in the value of the independent variablex. This equation can be used to predict y-values from x-values, with the understanding that some error will exist in predictions.
• If R²< 0.70, then the variablexis aPOORpredictor of the variabley. This equation should not be used to predict y-values from x-values.