The following are costs of advertising (in thousands of dollars)and the numbers of products sold (in thousands): $\begin{array} { c | r r r r r r r r }
Cost & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \
\hline Number & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}$
The equation of the regression line is $y = 2.78846 x + 55.7885$. Find the coefficient of determination.
A) $0.2353$
B) $0.5009$
C) $0.7077$
D) $- 0.0707$

Question

The following are costs of advertising (in thousands of dollars)and the numbers of products sold (in thousands): $\begin{array} { c | r r r r r r r r } 
Cost & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \
\hline Number & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}$
The equation of the regression line is $y = 2.78846 x + 55.7885$. Find the coefficient of determination.
A) $0.2353$
B) $0.5009$
C) $0.7077$
D) $- 0.0707$

Quizplus · Accepted Answer

The coefficient of determination, denoted as $R^2$, measures the proportion of the variance in the dependent variable that is predictable from the independent variable. It is calculated as the square of the correlation coefficient ($R$). Given the equation of the regression line $y = 2.78846x + 55.7885$, which indicates a positive linear relationship between the cost of advertising and the number of products sold, we can infer that the coefficient of determination must be a positive value that reflects the strength of this relationship. Among the given options, $0.5009$ is the only positive value that does not exceed 1, making it the correct choice for the coefficient of determination. Negative values or values greater than 1 are not valid for $R^2$.