The following are costs of advertising (in thousands of dollars) and the numbers of products sold (in thousands): $$\begin{array} { c | r r r r r r r r }
\text { Cost } & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \
\hline \text { Number } & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}$$ The equation of the regression line is ^y = 2.78846x + 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): $$\begin{array} { c | r r r r r r r r } 
\text { Cost } & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \
\hline \text { Number } & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73
\end{array}$$ The equation of the regression line is ^y = 2.78846x + 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 R², is the square of the correlation coefficient (r). It represents the proportion of the variance in the dependent variable that is predictable from the independent variable. In this case, the correct R² value is 0.5009, indicating that approximately 50.09% of the variance in the number of products sold can be explained by the advertising cost.

The Following Are Costs of Advertising (In Thousands of Dollars)