1. The question asks to choose a data point in our graph (we chose 476,44) of median home prices (x) and percentage of students who scored Advanced on math MCAS (y).
We have to find the residual. I'm confused because the equation I was given is e=y-yhat
I know one is the expected value and one is what we got.
What do I plug in for y and what do I plug in for yhat?
The value of Rsquared is .72 on the calculator and if you square it it's .5184. Do I need to do anything with Rsquared or is that not involved in the residual?
2. Explain what residual measures?
1. To find the residual, you need to first have a linear regression equation that relates the independent variable (x) to the dependent variable (y). In this case, it seems that the equation you were given is in the form of e = y - ŷ, where e represents the residual, y is the actual observed value, and ŷ is the predicted value based on the regression equation.
To find the residual for a specific data point, you need to substitute the corresponding values for y and ŷ into the equation. In this case, if you have chosen the data point (476, 44) as you mentioned, plug in 44 for y (actual value) and calculate ŷ (the predicted value) using the regression equation. Then, substitute these values into the formula e = y - ŷ to find the residual.
Regarding the value of R-squared, it measures the proportion of the total variation in the dependent variable (y) that can be explained by the independent variable (x) in the regression model. The R-squared value itself does not directly come into play when calculating the residuals. However, it is helpful as an overall measure of how well the regression model fits the data.
2. The residual measures the difference between the observed or actual value of the dependent variable and the predicted value based on the regression equation. In other words, it represents the vertical distance between the data point and the regression line. The residual provides information on the magnitude and direction of the discrepancy between the observed value and what would be expected based on the regression model. By examining the residuals, you can assess the accuracy and precision of the model's predictions.