/*! 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 4 Explain the difference between l... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 13: Problem 4

Explain the difference between linear and nonlinear relationships between two variables.

Short Answer

Expert verified
A linear relationship is when an increase or decrease in one variable leads to a consistent increase or decrease in another variable, forming a straight line on a graph. A nonlinear relationship is when the rate of change between the two variables isn't consistent, leading to a curve on a graph.

Step by step solution

01

Definition of Linear Relationships

A linear relationship between two variables is when one variable increases or decreases, the other variable also increases or decreases at a consistent rate. This forms a straight line when plotted on a graph. The equation can be written in the form of \(y = mx + b\), where \(m\) is the slope of the line (representing the rate of change) and \(b\) is the y-intercept.
02

Definition of Nonlinear Relationships

A nonlinear relationship between two variables is when one variable increases or decreases, the other variable doesn't change at a consistent rate, meaning the rate of change varies. Nonlinear relationships don't form a straight line when plotted on a graph but curve instead. The equation can take many forms, such as quadratic (\(y = ax^2 + bx + c\)), exponential (\(y = a^x\)), logarithmic (\(y = a\ln(x) + b\)) etc.
03

Comparison

In comparison, linear relationships have a constant rate of change, forming a straight line on a graph, and the relationship can be defined by two parameters - the slope and y-intercept. On the other hand, non-linear relationships have a variable rate of change, forming curves on a graph, and their equations can be more complex depending on the nature of the relationship.

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 91影视!

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

Explain the difference between a simple and a multiple regression model.

Two variables \(x\) and \(y\) have a negative linear relationship. Explain what happens to the value of \(y\) when \(x\) increases.

The following table, reproduced from Exercise \(13.26\), gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 13 varieties of Kellogg's cereal. $$ \begin{array}{l|rrrrrrrrrrrrr} \hline \text { Sugar (grams) } & 4 & 15 & 12 & 11 & 8 & 6 & 7 & 2 & 7 & 14 & 20 & 3 & 13 \\ \hline \text { Calories } & 120 & 200 & 140 & 110 & 120 & 80 & 190 & 100 & 120 & 190 & 190 & 110 & 120 \\ \hline \end{array} $$ a. Determine the standard deviation of errors. b. Find the coefficient of determination and give a brief interpretation of it.

Suppose that you work part-time at a bowling alley that is open daily from noon to midnight. Although business is usually slow from noon to 6 P.M., the owner has noticed that it is better on hotter days during the summer, perhaps because the premises are comfortably air-conditioned. The owner shows you some data that she gathered last summer. This data set includes the maximum temperature and the number of lines bowled between noon and 6 P.M. for each of 20 days. (The maximum temperatures ranged from \(77^{\circ} \mathrm{F}\) to \(95^{\circ} \mathrm{F}\) during this period.) The owner would like to know if she can estimate tomorrow's business from noon to 6 P.M. by looking at tomorrow's weather forecast. She asks you to analyze the data. Let \(x\) be the maximum temperature for a day and \(y\) the number of lines bowled between noon and 6 P.M. on that day. The computer output based on the data for 20 days provided the following results: \(\hat{y}=-432+7.7 x, \quad s_{e}=28.17, \quad \mathrm{SS}_{x x}=607, \quad\) and \(\quad \bar{x}=87.5\) Assume that the weather forecasts are reasonably accurate. a. Does the maximum temperature seem to be a useful predictor of bowling activity between noon and 6 P.M.? Use an appropriate statistical procedure based on the information given. Use \(\alpha=.05\) b. The owner wants to know how many lines of bowling she can expect, on average, for days with a maximum temperature of \(90^{\circ}\). Answer using a \(95 \%\) confidence level. c. The owner has seen tomorrow's weather forecast, which predicts a high of \(90^{\circ} \mathrm{F}\). About how many lines of bowling can she expect? Answer using a \(95 \%\) confidence level. d. Give a brief commonsense explanation to the owner for the difference in the interval estimates of parts \(\mathrm{b}\) and \(\mathrm{c}\). e. The owner asks you how many lines of bowling she could expect if the high temperature were \(100^{\circ} \mathrm{F}\). Give a point estimate, together with an appropriate warning to the owner.

The following information is obtained for a sample of 80 observations taken from a population. $$ \mathrm{SS}_{x x}=380.592, \quad s_{e}=.961, \text { and } \hat{y}=160.24-2.70 x $$ a. Make a \(97 \%\) confidence interval for \(B\). b. Test at the \(1 \%\) significance level whether \(B\) is negative. c. Can you conclude that \(B\) is different from zero? Use \(\alpha=.01\). d. Using a significance level of 02, test whether \(B\) is less than \(-1,25\).
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation
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.