Question

Social scientists are interested in the association between high school graduation rate (HSGR, measured as a percent) and the percent 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 ${\mathrm{POV}}^{\wedge }=59.2-0.620$(HSGR) $\widehat{\mathrm{POV}}=59.2-0.620$(HSGR) with $\mathrm{r}2=0.802r^2=0.802$. 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 percent of families living in poverty is predicted to decrease by approximately 0.896 .

b. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.802.

c. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.620.

d. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.802.

e. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.620.

Short answer

c. The percentage of poor families is expected to fall by $0.620$ for every one percent improvement in graduation rates.

Step-by-step solution

Given Information

Given,

The value of slope is $0.620$

Explanation for correct option

When the slope of the regression line is calculated, it is discovered that it is negative, indicating an inverse association between poverty and high school graduation rate. It is discovered that a, b, and d do not use the slope value.

As a result, the correct option is (c)

Explanation for incorrect option

a. For each 1% increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.896 is not the best interpretation for the slope of the least-squares regression line .

b. For each 1 % increase in the graduation rate, the percent of families living in poverty is predicted to decrease by approximately 0.802 is not the best interpretation for the slope of the least-squares regression line .

d. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.802 is not the best interpretation for the slope of the least-squares regression line .

e. For each 1 % increase in the percent of families living in poverty, the graduation rate is predicted to decrease by approximately 0.620 is not the best interpretation for the slope of the least-squares regression line .