Read the following description of a data set.A soccer coach is considering a strategy of having defensive players take more shots on goal. She evaluated a sample of her team's recent matches to see how players in defensive roles could contribute offensively.In each match the coach tracked the number of shots on goal by her defenders, x. She also noted the difference between the number of goals that had been scored by her team and the opposing team, y.The least squares regression line of this data set is:y=0.456x+3.075Complete the following sentence:For each additional shot on goal by the defenders, the least squares regression line predicts an increase of __ in the goal difference.
Q. Read the following description of a data set.A soccer coach is considering a strategy of having defensive players take more shots on goal. She evaluated a sample of her team's recent matches to see how players in defensive roles could contribute offensively.In each match the coach tracked the number of shots on goal by her defenders, x. She also noted the difference between the number of goals that had been scored by her team and the opposing team, y.The least squares regression line of this data set is:y=0.456x+3.075Complete the following sentence:For each additional shot on goal by the defenders, the least squares regression line predicts an increase of __ in the goal difference.
Identify Slope: Identify the slope of the least squares regression line.The equation given is y=0.456x+3.075. The slope of the least squares regression line is the coefficient of x, which is 0.456. This slope represents the change in the predicted value of y for each one-unit increase in x.
Interpret Slope: Interpret the slope in the context of the problem.In the equation y=0.456x+3.075, x represents the number of shots on goal by defenders, and y represents the goal difference (goals scored by the team minus goals scored by the opposing team). The slope of 0.456 indicates that for each additional shot on goal by a defender, the least squares regression line predicts an increase of 0.456 in the goal difference.