Read the following description of a data set.A gym franchise was considering a television marketing campaign to increase its membership. The franchise's market researchers wanted to get a better sense of the television and exercise habits of the gym's target demographic. To begin, the market researchers surveyed some of the current members about how many hours they had spent watching television and exercising last month.Using the survey responses, the researchers compared the number of hours of television watched, x, to the number of hours of exercise, y, for each member.The least squares regression line of this data set is:y=−0.105x+26.138Complete the following sentence:If a gym member had watched one additional hour of television last month, the least squares regression line predicts that they would have spent ___ hours less exercising that month.
Q. Read the following description of a data set.A gym franchise was considering a television marketing campaign to increase its membership. The franchise's market researchers wanted to get a better sense of the television and exercise habits of the gym's target demographic. To begin, the market researchers surveyed some of the current members about how many hours they had spent watching television and exercising last month.Using the survey responses, the researchers compared the number of hours of television watched, x, to the number of hours of exercise, y, for each member.The least squares regression line of this data set is:y=−0.105x+26.138Complete the following sentence:If a gym member had watched one additional hour of television last month, the least squares regression line predicts that they would have spent ___ hours less exercising that month.
Equation Analysis: The equation given is y=−0.105x+26.138. The slope of the least squares regression line is the coefficient of x, which is −0.105.
Interpretation of Slope: In the equation y=−0.105x+26.138, x represents the number of hours of television watched, and y represents the number of hours of exercise. The slope of −0.105 indicates that for each one hour increase in the number of hours of television watched, a gym member would spend 0.105 hours less exercising.