Question

In each of the following cases, find the best predicted value for y given that x = 3.00. The given statistics are summarized from paired sample data. Use the given data to find the best predicted value of the dependent variable. Be sure to follow the prediction procedures.

r = 0.988, y = 7.00, n = 20, and the equation of the regression line is y hat = 6.00 + 5.00x.

Answer 1

To find the predicted value of y for x = 3.00 using the given regression equation y hat = 6.00 + 5.00x, you plug in x into the equation to get y hat = 6.00 + 15.00 = 21.00. Therefore, the best predicted value for y is 21.00.

Step-by-step explanation:

The question involves using regression analysis to predict the value of a dependent variable (y) based on the given value of an independent variable (x). This is a common task in statistics, where the relationship between two variables is determined using a set of paired sample data. The line of best fit is an equation derived from such data, used to make predictions.

For the student's scenario, we have been given the equation of the regression line as ≚ = 6.00 + 5.00x, and we seek the predicted value of y when x is 3.00. Substituting the known value of x into the equation, we get the predicted value ≚ = 6.00 + 5.00(3.00) = 6.00 + 15.00 = 21.00. Therefore, the best-predicted value for y when x is 3.00 in this case would be 21.00.