L11046 X y 11.46 Consider the following pairs of observations: 1 1 4 3 3 3 2 1 5 4 6 7 0 2 a. Construct a scatterplot for the data. b. Use the method of least squares to fit a straight line to the seven data points in the table. c. Plot the least squares line on your scatterplot of part a.
L11046 X y 11.46 Consider the following pairs of observations: 1 1 4 3 3 3 2 1 5 4 6 7 0 2 a. Construct a scatterplot for the data. b. Use the method of least squares to fit a straight line to the seven data points in the table. c. Plot the least squares line on your scatterplot of part a.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![## Problem 11.46
Consider the following pairs of observations:
\[
\begin{array}{c|ccccccc}
x & 1 & 4 & 3 & 2 & 5 & 6 & 0 \\
\hline
y & 1 & 3 & 3 & 1 & 4 & 7 & 2 \\
\end{array}
\]
### Tasks:
a. **Construct a scatterplot for the data.**
b. **Use the method of least squares to fit a straight line to the seven data points in the table.**
c. **Plot the least squares line on your scatterplot from part a.**
d. **Specify the null and alternative hypotheses you would use to test whether the data provide sufficient evidence to indicate that \( x \) contributes information for the (linear) prediction of \( y \).**
e. **What is the test statistic that should be used in conducting the hypothesis test of part d? Specify the degrees of freedom associated with the test statistic.**
f. **Conduct the hypothesis test of part d using \( \alpha = .05 \).**
(Note: Graphs and plots are required to visually represent data relationships and fits, although they cannot be displayed in this text description.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa133d66-10ad-45c9-aebb-4433e2c2921a%2Fab8daaba-173c-473f-bce4-6455942f0c90%2F27lwfkb_processed.png&w=3840&q=75)
Transcribed Image Text:## Problem 11.46
Consider the following pairs of observations:
\[
\begin{array}{c|ccccccc}
x & 1 & 4 & 3 & 2 & 5 & 6 & 0 \\
\hline
y & 1 & 3 & 3 & 1 & 4 & 7 & 2 \\
\end{array}
\]
### Tasks:
a. **Construct a scatterplot for the data.**
b. **Use the method of least squares to fit a straight line to the seven data points in the table.**
c. **Plot the least squares line on your scatterplot from part a.**
d. **Specify the null and alternative hypotheses you would use to test whether the data provide sufficient evidence to indicate that \( x \) contributes information for the (linear) prediction of \( y \).**
e. **What is the test statistic that should be used in conducting the hypothesis test of part d? Specify the degrees of freedom associated with the test statistic.**
f. **Conduct the hypothesis test of part d using \( \alpha = .05 \).**
(Note: Graphs and plots are required to visually represent data relationships and fits, although they cannot be displayed in this text description.)
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