Questions: Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) a certain pharmaceutical drug and the number of prescriptions written (in thousands): Cost of Advertising: 9, 2, 3, 4, 2, 5, 9, 10 Number of Prescriptions: 85, 52, 55, 68, 67, 86, 83, 73 0.235 0.246 -0.071 0.708

Find the value of the linear correlation coefficient r. The paired data below consist of the costs of advertising (in thousands of dollars) a certain pharmaceutical drug and the number of prescriptions written (in thousands): Cost of Advertising: 9, 2, 3, 4, 2, 5, 9, 10 Number of Prescriptions: 85, 52, 55, 68, 67, 86, 83, 73 0.235 0.246 -0.071 0.708
Transcript text: Find the value of the linear correlation coefficient $r$. The paired data below consist of the costs of advertising (in thousands of dollars) a certain pharmaceutical drug and the number of prescriptions written (in thousands): \begin{tabular}{l|r|r|r|r|r|r|r|r} \begin{tabular}{l} Cost of \\ Advertising \end{tabular} & 9 & 2 & 3 & 4 & 2 & 5 & 9 & 10 \\ \hline \begin{tabular}{l} Number of \\ Prescriptions \end{tabular} & 85 & 52 & 55 & 68 & 67 & 86 & 83 & 73 \end{tabular} 0.235 0.246 $-0.071$ 0.708
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate Covariance

The covariance between the cost of advertising \( X \) and the number of prescriptions written \( Y \) is calculated as follows:

\[ \text{Cov}(X,Y) = 31.071 \]

Step 2: Calculate Standard Deviations

Next, we calculate the standard deviations of both variables:

\[ \sigma_X = 3.338 \]

\[ \sigma_Y = 13.152 \]

Step 3: Calculate Correlation Coefficient

The correlation coefficient \( r \) is computed using the formula:

\[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \]

Substituting the values we have:

\[ r = \frac{31.071}{3.338 \times 13.152} = 0.708 \]

Final Answer

The correlation coefficient \( r \) is given by:

\[ \boxed{r = 0.708} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
The functions (f) and (g) are defined as follows. [ f(x)=fracx+7x^2-49 ] [ g(x)=fracxx^2+9 ] For each function, find the domain. Write each answer as an interval or union of intervals. Domain of (f) : (square) Domain of (g) : (square)
failedAnswered
Problem 7: (3% of Assignment Value) Please answer the following questions about uniform circular motion. - Part (a) v A planet orbits a star in a circular orbit at a constant orbital speed. Which of the following statements is true? The planet experiences a centripetal force pulling towards its star. Correct! - Part (b) v When a planet is orbiting a star, which force plays the role of the centripetal force? The gravitational force. Correct! - Part (c) v Which of the following statements about uniform circular motion is true? An object in uniform circular motion experiences a centripetal force. Correct! Part (d) A student swings a ball on a string in a circle at a constant speed, then suddenly lets go of the string. When the student lets go of the string, what happens from a physics standpoint? The centripetal force disappears. A tangential force stops acting on the ball. A tangential force starts acting on the ball. A centripetal force starts acting on the ball. Nothing happens from the standpoint of physics. None of these are correct.
failedAnswered
Determine the domain and range of the graph.
failedAnswered
Find the midpoint of the segment with the following endpoints. (9,1) and (2,9)
failedAnswered
Which need refers to someone feeling connected with others?