In: Statistics and Probability
9) Use the following data to estimate a linear regression equation between y and x. Interpret the estimated slope coefficient. Predict y for an x value of 9. Calculate and interpret the model’s R-squared.
| x | y |
| 21 | 12 |
| 17 | 10 |
| 11 | 8 |
| 3 | 5 |
| 13 | 15 |

Here we get slope = 0.380 (Rounded to three decimal places)
It represents if we change the value of x then the value of y will be changed by 0.380
For x = 9 we get y^ = 8.478 (Rounded to three decimal places)
We get R2 = 0.4591
It represents the proportion of variance explained by x in y.
Here 45.91% proportion of variance explained by x in y.
Hope this will help you. Thank you :)