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Social scientists are interested in the association between the high school graduation rate (HSGR) and the percentage of U.S. families living in poverty (POV). Data were collected from all $50$states and the District of Columbia, and a regression analysis was conducted. The resulting least-squares regression line is given by $\overline{POV}=59.2-0.620$(HSGR) with $r^2=0.802$. Based on the information, which of the following is the best interpretation for the slope of the least-squares regression line?

(a) For each $1\%$increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately $0.896$.

(b) For each $1\%$increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately $0.802$.

(c) For each $1\%$increase in the graduation rate, the per cent of families living in poverty is predicted to decrease by approximately $0.620$.

(d) For each$1\%$increase in the percentage of families living in poverty, the graduation rate is predicted to increase by approximately $0.802$.

(e) For each $1\%$increase in the per cent of families living in poverty, the graduation rate is predicted to decrease by approximately$0.620$.

Step by step solution

01

Given information

Data were collected from all $50$states

The least-squares regression line is given by $\overline{POV}=59.2-0.620$(HSGR) with $r^2=0.802$

To find the best interpretation for the slope of the least-squares regression line.

02

Explanation

Determine the regression line's slope; observe that it is negative, indicating a negative association between high school graduation rate and poverty (as graduation rate increases, poverty decreases; graduation rate decreases, poverty increases)

Slope $=-0.620$

Notice answers a, b, and d are not using the value of the slope. This leaves only two answers

Remove option e

The slope is calculated as follows: for every unit increase in X, the slope value of 0.620 decreases Y. (decreased since negative). In this scenario, X represents the high school graduation rate and Y represents the poverty rate. Part e is a mash-up, and the correct answer is (c).

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