(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x an the least-squares line? What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) r2 = 0.8506 91.4 explained 8.6 X % unexplained (f) Suppose a pharmaceutical company has 17 different research programs. What does the least-squares equation forecast for y = mean number of patents per program? (Round your answer to two decimal places.) X patents per program 1.42
(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x an the least-squares line? What percentage is unexplained? (Round your answer for r2 to four decimal places. Round your answers for the percentages to two decimal place.) r2 = 0.8506 91.4 explained 8.6 X % unexplained (f) Suppose a pharmaceutical company has 17 different research programs. What does the least-squares equation forecast for y = mean number of patents per program? (Round your answer to two decimal places.) X patents per program 1.42
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![The text discusses a scenario in which the variable \( x \) represents the number of different research programs, and \( y \) represents the mean number of patents per program. It notes that having too many research programs can lead to a decline in overall research productivity. The data presented is related to pharmaceutical companies and their research programs.
Data Table:
\[
\begin{array}{c|c}
x & y \\
\hline
10 & 1.8 \\
12 & 1.5 \\
14 & 1.7 \\
16 & 1.4 \\
18 & 1.0 \\
20 & 0.7 \\
\end{array}
\]
The accompanying calculations are:
- \(\Sigma x = 90\),
- \(\Sigma y = 8.1\),
- \(\Sigma x^2 = 1420\),
- \(\Sigma y^2 = 11.83\),
- \(\Sigma xy = 114.2\),
- \(r \approx -0.9223\).
A scatter diagram is drawn to visually display this data, plotting the number of research programs (x-axis) against the mean number of patents per program (y-axis). The points show a downward trend indicating a negative correlation, consistent with the calculated correlation coefficient \( r \approx -0.9223 \), suggesting a strong negative relationship. As the number of research programs increases, the mean number of patents per program decreases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00154cd9-82c7-455b-845c-02cf21fdb65c%2F4700e1ca-0b1d-4e40-b86c-cfe81c1575e1%2F0dta1rm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The text discusses a scenario in which the variable \( x \) represents the number of different research programs, and \( y \) represents the mean number of patents per program. It notes that having too many research programs can lead to a decline in overall research productivity. The data presented is related to pharmaceutical companies and their research programs.
Data Table:
\[
\begin{array}{c|c}
x & y \\
\hline
10 & 1.8 \\
12 & 1.5 \\
14 & 1.7 \\
16 & 1.4 \\
18 & 1.0 \\
20 & 0.7 \\
\end{array}
\]
The accompanying calculations are:
- \(\Sigma x = 90\),
- \(\Sigma y = 8.1\),
- \(\Sigma x^2 = 1420\),
- \(\Sigma y^2 = 11.83\),
- \(\Sigma xy = 114.2\),
- \(r \approx -0.9223\).
A scatter diagram is drawn to visually display this data, plotting the number of research programs (x-axis) against the mean number of patents per program (y-axis). The points show a downward trend indicating a negative correlation, consistent with the calculated correlation coefficient \( r \approx -0.9223 \), suggesting a strong negative relationship. As the number of research programs increases, the mean number of patents per program decreases.
![**Graph Description**:
The graph displays a scatter plot and a linear regression line, illustrating the relationship between the number of different research programs (\(x\)) and the mean number of patents (\(y\)). The x-axis ranges from 0.8 to 1.8, while the y-axis ranges from 10 to 18.
**Text Transcription**:
(e) Find the value of the coefficient of determination \(r^2\). What percentage of the variation in \(y\) can be *explained* by the corresponding variation in \(x\) and the least-squares line? What percentage is *unexplained*? (Round your answer for \(r^2\) to four decimal places. Round your answers for the percentages to two decimal places.)
\[
r^2 = 0.8506 \quad \text{✔}
\]
\[
\text{explained} \quad 91.4 \quad \text{✘} \quad \%
\]
\[
\text{unexplained} \quad 8.6 \quad \text{✘} \quad \%
\]
(f) Suppose a pharmaceutical company has 17 different research programs. What does the least-squares equation forecast for \(y = \text{mean number of patents per program}\)? (Round your answer to two decimal places.)
\[
\text{1.42} \quad \text{✘} \quad \text{patents per program}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00154cd9-82c7-455b-845c-02cf21fdb65c%2F4700e1ca-0b1d-4e40-b86c-cfe81c1575e1%2Fhlnhkcr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph Description**:
The graph displays a scatter plot and a linear regression line, illustrating the relationship between the number of different research programs (\(x\)) and the mean number of patents (\(y\)). The x-axis ranges from 0.8 to 1.8, while the y-axis ranges from 10 to 18.
**Text Transcription**:
(e) Find the value of the coefficient of determination \(r^2\). What percentage of the variation in \(y\) can be *explained* by the corresponding variation in \(x\) and the least-squares line? What percentage is *unexplained*? (Round your answer for \(r^2\) to four decimal places. Round your answers for the percentages to two decimal places.)
\[
r^2 = 0.8506 \quad \text{✔}
\]
\[
\text{explained} \quad 91.4 \quad \text{✘} \quad \%
\]
\[
\text{unexplained} \quad 8.6 \quad \text{✘} \quad \%
\]
(f) Suppose a pharmaceutical company has 17 different research programs. What does the least-squares equation forecast for \(y = \text{mean number of patents per program}\)? (Round your answer to two decimal places.)
\[
\text{1.42} \quad \text{✘} \quad \text{patents per program}
\]
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