Read the following description of a data set.A graduate school rates entrance applications on a scale of 1 to 10, where 10 is excellent. Administrators are curious to know whether the application rating can be used to predict the number of years it will take an admitted student to graduate.For the students graduating this year, the administrators note the ratings of their applications, x, as well as the number of years it took them to graduate, y.The least squares regression line of this data set is:y=−0.617x+12.718Complete the following sentence:If a student's application was rated one point higher, the least squares regression line predicts it would take him or her __ fewer years to graduate.
Q. Read the following description of a data set.A graduate school rates entrance applications on a scale of 1 to 10, where 10 is excellent. Administrators are curious to know whether the application rating can be used to predict the number of years it will take an admitted student to graduate.For the students graduating this year, the administrators note the ratings of their applications, x, as well as the number of years it took them to graduate, y.The least squares regression line of this data set is:y=−0.617x+12.718Complete the following sentence:If a student's application was rated one point higher, the least squares regression line predicts it would take him or her __ fewer years to graduate.
Identify Slope: Identify the slope of the least squares regression line.The equation given is y=−0.617x+12.718. The slope of the least squares regression line is the coefficient of x, which is −0.617. This slope indicates the change in the number of years it takes to graduate (y) for each one-point increase in the application rating (x).
Interpret Slope: Interpret the slope.Since the slope is −0.617, this means that for each one-point increase in the application rating, the least squares regression line predicts that it will take 0.617 fewer years to graduate.