Discuss one of the following:
(1) Using paired height and pulse rate data for females we determine the regression equation to be ŷ = 73.9 + 1.0223(x), where x represents height (cm). Discuss what the symbol ŷ represents, and explain what the predictor variable represents and what the response variable represents
(2) Discuss how you determine if the regression equation is a good model and if it is how you would find the predicted value of y. Also discuss what the best predicted value of y would be if the regression equation is not a good model.
To determine if the regression model is a good model we look at the residuals.
(We assume that the scatterplot of the data looked appropriately "linear", that the correlation coefficient r was calculated and found to be significant, and that all of the assumptions (such as x and y having bivariate normality) have been met.)
Calculate the residuals (y-y-hat) and plot on a residual chart. We look at how the residuals change as x increases.
If as x increases the residuals are close to 0 then the model will be good. If the residuals get larger(or smaller) as x increases or if the plot of the residuals is not linear the model will not be good for predictions.
Assuming that the model will be a good predictor, substitute x into the regression equation to get the predicted value for y. (In other words, use the y values on the regression line as the predicted values.)
If the model is not a good predictor, we use the mean value of the y's as the predicted value.