Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Q3E (page 649)

The equation for a straight line (deterministic model) is

y=β0+β1x

If the line passes through the point (-2, 4), then x = -2, y = 4 must satisfy the equation; that is,

4=β0+β1(-2)

Similarly, if the line passes through the point (4, 6), then x = 4, y = 6 must satisfy the equation; that is,

6=β0+β1(4)

Use these two equations to solve for and ; then find the equation of the line that passes through the points (-2, 4) and (4, 6).

Short Answer

Expert verified

β0=143, β1=-13

3y = 14 + x

Step by step solution

01

Introduction

In geometry, a line is essentially a zero-width object that extends on both sides. A straight line is a line that does not have any curves. A straight line is one that has no curves and extends to both sides to infinity.

02

Finding  β0 and β1

Equation of a straight line:

y=β0+β1x

If a line passes through, (2, 4),

4=β0+β1(-2).........(1)

If a line passes through (4, 6),

6=β0+β1(4).........(2)

Solving equations (1) & (2) simultaneously, we get

β0+β1(-2)-4=β0+β1(4)-66β1=-2β1=-26β1=-13

Therefore, we get

4=β0+-13(-2)4+23=β0β0=12+23β0=143

03

Finding the equation that passes through the points (-2, 4) and (4, 6) 

y=β0+β1xy=143+13xy=14+x33y=14+x

Therefore, the required equation is 3y = 14 + x.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Give the slope and y-intercept for each of the lines graphed in Exercise 11.1.

Refer to Exercise 11.3. Find the equations of the lines that pass through the points listed in Exercise 11.1.

Best-paid CEOs. Refer to Glassdoor Economic Research firm’s 2015 ranking of the 40 best-paid CEOs in Table 2.1 (p. 65). Recall that data were collected on a CEO’s age and ratio of salary to a typical worker’s pay at the firm. One objective is to predict the ratio of salary to worker pay based on the CEO’s age.

a. In this study, identify the dependent and independent variables.

b. Explain why a probabilistic model is more appropriate than a deterministic model.

c. Write the equation of the straight-line, probabilistic model.

Generation Y’s entitlement mentality. The current workforce is dominated by “Generation Y”—people born between 1982 and 1999. These workers have a reputation as having an entitlement mentality (e.g., they believe they have a right to a high-paying job, without the work ethic). The reasons behind this phenomenon were investigated in Proceedings of the Academy of Educational Leadership (Vol. 16, 2011). A sample of 272 undergraduate business students was administered a questionnaire designed to capture the behaviors that lead to an entitlement mentality. The responses were used to measure the following two quantitative variables for each student: entitlement score (y)—where higher scores indicate a greater level of entitlement, and “helicopter parents” score (x)—where higher scores indicate that the student’s parents had a higher level of involvement in his or her everyday experiences and problems.

a. Give the equation of a simple linear regression model relating y to x.

b. The researchers theorize that helicopter parents lead to an entitlement mentality. Based on this theory, would you expect β0 to be positive or negative (or are you unsure)? Would you expect β1 to be positive or negative (or are you unsure)? Explain.

c. The p-value for testing H0: β0 = 0 versus Ha: β1> 0 was reported as .002. Use this result to test the researchers’ entitlement theory at α = .01.

Voltage sags and swells. The power quality of a transformer is measured by the quality of the voltage. Two causes of poor power quality are "sags" and "swells." A sag is an unusual dip and a swell is an unusual increase in the voltage level of a transformer. The power quality of transformers built in Turkey was investigated in Electrical Engineering (Vol. 95, 2013). For a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184. Assume the standard deviation of the sag distribution is 30 sags per week and the standard deviation of the swell distribution is 25 swells per week.

a. For a sag distribution with any shape, what proportion of transformers will have between 263 and 443 sags per week? Which rule did you apply and why?

b. For a sag distribution that is mound-shaped and symmetric, what proportion of transformers will have between 263 and 443 sags per week? Which rule did you apply and why?

c. For a swell distribution with any shape, what proportion of transformers will have between 109 and 259 swells per week? Which rule did you apply and why?

d. For a swell distribution that is mound-shaped and symmetric, what proportion of transformers will have between 109 and 259 swells per week? Which rule did you apply and why?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

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.

Sign-up for free