Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Q. T12.3 (page 824)

T12.3 Inference about the slope β1 of a least-squares regression line is based on which of
the following distributions?
a. The tdistribution with n−1 degrees of freedom
b. The standard Normal distribution
c. The chi-square distribution with n−1 degrees of freedom
d. The t distribution with n-2 degrees of freedom
e. The Normal distribution with mean μ and standard deviation σ.

Short Answer

Expert verified

The correct answer is option (d) The tdistribution with n-2 degrees of freedom.

Step by step solution

01

Given information

To inference about the slope β1 of a least-squares regression line is based on which of the following distributions.

02

Explanation

To figure out the below distributions biases inference about a least-squares regression line's slope β1.
To establish the least square regression line, two parameters must be estimated: the y-intercept and the slope.
The t-distribution with degrees of freedom equal to the sample size n minus the number of calculated parameters becomes the appropriate distribution.
As a result,
df=n-2
Therefore, the correct answer is option (d).

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

The swinging pendulum Mrs. Hanrahan's precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-and-forth swing (called it's period). The theoretical relationship between a pendulum's length and its period is

period=2πglength

where gis a constant representing the acceleration due to gravity (in this case, g=980cm/s2g=980cm/s2). Here is a graph of the period versus length, length, along with output from a linear regression analysis using these variables.

a. Give the equation of the least-squares regression line. Define any variables you use.

b. Use the model from part (a) to predict the period of a pendulum with length 80cm.

T12.10We record data on the population of a particular country from 1960 to 2010. A
scatterplot reveals a clear curved relationship between population and year. However, a different scatterplot reveals a strong linear relationship between the logarithm (base 10) of the population and the year. The least-squares regression line for the transformed data is
log(population)=^−13.5+0.01(year)
Based on this equation, which of the following is the best estimate for the population of the country in the year 2020?
a. 6.7
b. 812
c. 5,000,000
d. 6,700,000
e. 8,120,000

Which sampling method was used in each of the following settings, in order from I to IV?

I. A student chooses to survey the first 20 students to arrive at school.

II. The name of each student in a school is written on a card, the cards are well mixed, and 10 names are drawn.

III. A state agency randomly selects 50 people from each of the state’s senatorial districts.

IV. A city council randomly selects eight city blocks and then surveys all the voting-age residents on those blocks.

a. Voluntary response, SRS, stratified, cluster

b. Convenience, SRS, stratified, cluster

c. Convenience, cluster, SRS, stratified

d. Convenience, SRS, cluster, stratified

e. Cluster, SRS, stratified, convenience

A researcher from the University of California, San Diego, collected data on average per capita wine consumption and heart disease death rate in a random sample of 19 countries for which data were available. The following table displays the data

Is there convincing evidence of a negative linear relationship between wine consumption and heart disease deaths in the population of countries?

T12.11 Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15 chickens, 3 chickens were randomly assigned to each of 5 different doses of growth hormone (0, 0.2, 0.4, 0.8, and 1.0 milligrams). The subsequent weight gain (in ounces) was recorded for each chicken. A researcher plots the data and finds that a linear relationship appears to hold. Here is computer output from a least-squares
regression analysis of these data. Assume that the conditions for performing inference about the slope β1of the true regression line are met.

a. Interpret each of the following in context:
i. The slope
ii. The y intercept
iii. The standard deviation of the residuals
iv. The standard error of the slope
b. Do the data provide convincing evidence of a linear relationship between dose and weight gain? Carry out a significance test at the α=0.05 level.
c. Construct and interpret a 95%confidence interval for the slope parameter
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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