Question

Evaluating a regression model: A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y = − 0.693 ⋅ x + 28.802 , with an R-squared value of 0.571536. Assume the model indicates a significant relationship between hours of TV watched and the number of situps a person can do. Use the model to predict the number of situps a person who watches 6 hours of TV can do (to one decimal place).

Answer 1

The predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.

The given results of regression:

y = –0.693x + 28.802

The formula for regression equation is:

y = ax + b

So, given that:

a = –0.693

b = 28.802

r2 = 0.571536

r = 0.756

Back to the given results of regression:

y = –0.693x + 28.802

In this case, y represents the number of sit-ups a person can do, and x represents the hours of TV watched per day.

Thus, the predicted number of sit-ups for a person who watches x = 6 hours of TV is:

y = –0.693x + 28.802

y = –0.693 * 6 + 28.802

y = –4.158 + 28.802

y = 24.644

Hence, the predicted number of sit-ups for a person who watches 6 hours of TV is 24.644.

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