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Interpret the least squares regression line of this 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.Hours of television Hours of exercise0.04 28.151.39 33.965.40 33.0424.16 20.6529.85 35.9337.44 7.7640.73 11.39The least squares regression line for the data set is:y=–0.466x+33.657Use it to complete 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.

Question

Interpret the least squares regression line of this 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.Hours of television Hours of exercise0.04 28.151.39 33.965.40 33.0424.16 20.6529.85 35.9337.44 7.7640.73 11.39The least squares regression line for the data set is:y=–0.466x+33.657Use it to complete 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.

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Solution

If a gym member had watched one additional hour of television last month, the least squares regression line predicts that they would have spent 0.466 hours less exercising that month.

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Critics of television often refer to the detrimental effects that all the violence shown on television has on children. However, there may be another problem. It may be that watching television also reduces the amount of physical exercise, causing weight gains.The following regression estimates show the relationship between the number of kilograms (in kgs) a child is overweight by, and the number of hours of television viewing per weekoverweight  =  0.55 +    0.13 hours (0.27)       (0.04)  Standard errors are shown in the brackets. The sample size is N=1800.Based on the regression results, how much does overweight change if the average number hours spent watching television is increased by 2 hours?Group of answer choicesIncrease by 0.26.Increase by 0.04.Increase by 0.13.Decrease by 0.13.

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