US public debt per capita historical data for the years 2009-2013 yields the following scatterplot: The equation of the regression line is predicted $($ Debt per capita $\$ \mathrm {~K} ) = - 6,975 + 3.49 \times ($ Debt Year $)$ with $R ^ { 2 } = 99.5 \%$. Which of the following statements is true?
A) About 99.5% of the variability in debt per capita is explained by the model.
B) On average, debt per capita increases $3.49K per year.
C) The response variable is "year."
D) Both A and B.
E) All of the above.

Question

US public debt per capita historical data for the years 2009-2013 yields the following scatterplot:  The equation of the regression line is predicted $($ Debt per capita $\$ \mathrm {~K} ) = - 6,975 + 3.49 \times ($ Debt Year $)$ with $R ^ { 2 } = 99.5 \%$. Which of the following statements is true?
A) About 99.5% of the variability in debt per capita is explained by the model. 
B) On average, debt per capita increases $3.49K per year. 
C) The response variable is "year." 
D) Both A and B. 
E) All of the above.

Quizplus · Accepted Answer

A) About 99.5% of the variability in debt per capita is explained by the model.
B) On average, debt per capita increases $3.49K per year.
C) The response variable is "year."
D) Both A and B.
E) All of the above.

B) On average, debt per capita increases $3.49K per year: This statement is true because the regression equation shows that for each year, the predicted debt per capita increases by $3.49K.

C) The response variable is "year": This statement is false because the year is the explanatory variable, not the response variable. The response variable is the debt per capita.

Therefore, the correct answer is D: Both A and B.

US Public Debt Per Capita Historical Data for the Years (((

US Public Debt Per Capita Historical Data for the Years $($