to illustrate the process for finding a linear regression equation by using technology: TI83/84 calculator; Excel; Statdisk.
We can use linear regression to make predictions if the variables have a strong correlation. This packet explores the relationship between brain size and IQ and determines if an IQ can be predicted from brain size - does a bigger brain size relate to a higher IQ? If it does, then we should be able to predict IQ based on brain size. If the correlation is not strong, then the best predictor of IQ would simply be the mean, 100.
Three technology solutions are presented. The first uses a TI84 calculator. The second shows how to do a trendline using Excel. The third video illustrates the solution using Statdisk, software that was developed by Mario Triola for his Elementary Statistics textbook.
The table gives brain sizes and IQs for 10 subjects. We want to find the best predicted IQ of someone with a brain size of 1275 cm^{3}.
Brain Size (cm^{3}) |
965 |
1029 |
1030 |
1285 |
1049 |
1077 |
1037 |
1068 |
1176 |
1105 |
IQ |
90 |
85 |
86 |
102 |
103 |
97 |
124 |
125 |
102 |
114 |
Should we use linear regression? We need to examine the data and decide whether regression is appropriate. If it is, we can obtain a prediction from the regression line. If it is not appropriate, we should simply use the mean IQ score as the best predictor.
Source: Elementary Statistics, 11th edition, Mario Triola
Determine the linear regression line for brain size vs. IQ using the data provided. Decide whether linear regression is appropriate. What is the best predictor of IQ in this case: brain size or mean IQ?
Use Excel to create a trendline -
Use Statdisk to do linear regression -
Based on the regression, with a brain size of 1275 cm^{3} we would predict an IQ of 71.8+0.0286(1275) = 108.
But since a linear relation is not supported, we would instead use the mean IQ score of 100 as the best predictor, independent of brain size.