AP Statistics Chapter 14 Section 1

The slope of the true regression line. The slope of the least squares regression line used to estimate The true intercept of the real regression line. The intercept of the least squares regression line – used as an unbiased estimator of

Linear Regression Inference Make a scatterplot of the data. Find the least squares regression line that fits the data. Place on graph with equation. Look for outliers or influential observations. Look at residuals to determine the fit of the prediction line. Look at r and r2. Write null and alternative hypotheses. Check assumptions Test statistic P-value Conclusion

How well do golfer’s scores in the first round of a tournament predict their scores in the second round? Golfer 1 2 3 4 5 6 7 8 9 10 11 12 Round 1 89 90 87 95 86 81 102 105 83 88 91 79 Round 2 94 85 76 107 80 100 90 80 80 90 100 Round 1

Round 2 vs Round 1 Residuals Based on the residual graph and the range of the residuals the use of this model for inference would be appropriate. The correlation coefficient and coefficient of determination are moderately strong as well.

Linear Regression Test Assumptions: For any fixed value of x, the response y varies according to a normal distribution. Repeated responses y are independent of each other. The mean response has a straight-line relationship with x. The slope and the intercept are unknown parameters The standard deviation of y is the same for all values.

Given that the slope is 0 the observed result will occur approx Given that the slope is 0 the observed result will occur approx. 1 out of every 100 times just by chance. Therefore this evidence rejects that the slope is 0.

We are 95% confident that for every unit of change in the first round of golf the score of the second round will change between -4 and 5 points.