/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 29 What diagnostic plot can you use... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

What diagnostic plot can you use to determine whether the incorrect model has been used? What should the plot look like if the correct model has been used?

Short Answer

Expert verified
Answer: A residuals versus fitted values plot, also called a residuals plot, can be used to determine whether an incorrect model has been used in a statistical analysis. If the correct model has been used, the plot should show random scatter, homoscedasticity, and an overall mean close to zero with no significant outliers.

Step by step solution

01

1. Identifying the Diagnostic Plot

A diagnostic plot commonly used to determine whether the correct model has been used is the residuals versus fitted values plot, also called a residuals plot. This plot shows the residuals, which are the differences between the observed values and the predicted values (fitted values), against the fitted values.
02

2. Analyzing Residuals Plot for the Correct Model

If the correct model has been used, the residuals plot should have the following characteristics: - There should be no clear pattern in the residuals; they should be scattered randomly. - The points should be homoscedastic, meaning the spread of the residuals should be consistent across the fitted values. - The overall mean of the residuals should be approximately zero. - There should be no significant outliers, meaning most of the points should be close to the horizontal line at zero.
03

3. Analyzing Residuals Plot for the Incorrect Model

If an incorrect model has been used, the residuals plot may exhibit the following characteristics: - There might be a clear pattern, and the residuals might not be distributed randomly. - The plot may show heteroscedasticity, meaning the spread of the residuals may not be consistent across the range of fitted values. - Large residuals or significant outliers might be present, indicating that the model is not accurately capturing the data. - Curvature in the plot may suggest that a nonlinear model would better describe the data. In conclusion, to determine whether the incorrect model has been used, one can use a residuals versus fitted values plot. If the correct model has been used, the plot should show random scatter, homoscedasticity, and an overall mean close to zero with no significant outliers. If these characteristics are not present, this may indicate that an incorrect model has been used.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You can refresh your memory about regression lines and the correlation coefficient by doing the MyApplet Exercises at the end of Chapter \(3 .\) a. Graph the line corresponding to the equation \(y=0.5 x+3\) by graphing the points corresponding to \(x=0,1,\) and 2 . Give the \(y\) -intercept and slope for the line. b. Check your graph using the How a Line Works applet.

Does a team's batting average depend in any way on the number of home runs hit by the team? The data in the table show the number of team home runs and the overall team batting average for eight selected major league teams for the 2006 season. \(^{14}\) $$ \begin{array}{lcc} \text { Team } & \text { Total Home Runs } & \text { Team Batting Average } \\\ \hline \text { Atlanta Braves } & 222 & .270 \\ \text { Baltimore Orioles } & 164 & .227 \\ \text { Boston Red Sox } & 192 & .269 \\ \text { Chicago White Sox } & 236 & .280 \\ \text { Houston Astros } & 174 & .255 \\ \text { Philadelphia Phillies } & 216 & .267 \\ \text { New York Giants } & 163 & .259 \\ \text { Seattle Mariners } & 172 & .272 \end{array} $$ a. Plot the points using a scatterplot. Does it appear that there is any relationship between total home runs and team batting average? b. Is there a significant positive correlation between total home runs and team batting average? Test at the \(5 \%\) level of significance. c. Do you think that the relationship between these two variables would be different if we had looked at the entire set of major league franchises?

In addition to increasingly large bounds on error, why should an experimenter refrain from predicting \(y\) for values of \(x\) outside the experimental region?

In Exercise 12.15 (data set EX1215), we measured the armspan and height of eight people with the following results: $$ \begin{array}{l|clll} \text { Person } & 1 & 2 & 3 & 4 \\ \hline \begin{array}{l} \text { Armspan (inches) } \\ \text { Height (inches) } \end{array} & 68 & 62.25 & 65 & 69.5 \\ & 69 & 62 & 65 & 70 \\ \text { Person } & 5 & 6 & 7 & 8 \\ \hline \text { Armspan (inches) } & 68 & 69 & 62 & 60.25 \\ \text { Height (inches) } & 67 & 67 & 63 & 62 \end{array} $$ a. Does the data provide sufficient evidence to indicate that there is a linear relationship between armspan and height? Test at the \(5 \%\) level of significance. b. Construct a \(95 \%\) confidence interval for the slope of the line of means, \(\beta\). c. If Leonardo da Vinci is correct, and a person's armspan is roughly the same as the person's height, the slope of the regression line is approximately equal to \(1 .\) Is this supposition confirmed by the confidence interval constructed in part b? Explain.

You are given these data: $$ \begin{array}{l|lllllll} x & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline y & 7 & 5 & 5 & 3 & 2 & 0 \end{array} $$ a. Plot the six points on graph paper. b. Calculate the sample coefficient of correlation \(r\) and interpret. c. By what percentage was the sum of squares of deviations reduced by using the least-squares predictor \(\hat{y}=a+b x\) rather than \(\bar{y}\) as a predictor of \(y ?\)

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.