What statistic is used to estimate

a. The y-intercept of the population regression line?

b. The slope of the population regression line?

c. The common conditional standard deviation, σ, of the response variable?

Short Answer

Expert verified

(a) β0is the y-intercept of line y=β0+6β1

(b) β1is the slope

(c) The standard error of the estimate is the statistic used to produce a point estimate for the common conditional standard deviation σ.

Step by step solution

01

Part (a) Step 1: Concept introduction

The mean squared discrepancies among both experimental and theoretical values is lessened by the regression line.

The linear regression relates the mean scores of the X and Y components.

02

Part (a) Step 2: Explanation

The y-intercept of the population regression line

β0Is the y-intercept of the population regression liney=β0+6β1.

03

Part (b) Step 1: Concept introduction

The mean squared discrepancies among both experimental and theoretical values is lessened by the regression line.

The linear regression relates the mean scores of the X and Y components.

04

Part (b) Step 2: Explanation

β1 is the slope of regression liney=β0+xβ1.

05

Part (c) Step 1: Concept introduction

The mean squared discrepancies among both experimental and theoretical values is lessened by the regression line.

The linear regression relates the mean scores of the X and Y components.

06

Part (c) Step 2: Explanation

The standard error of the estimate is the statistic used to produce a point estimate for the common conditional standard deviation σ.

Se=SSEn-2.

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 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

Suppose that x and y are predictor and response variables, respectively, of a population. Consider the population that consists of all members of the original population that have a specified value of the predictor variable. The distribution, mean, and standard deviation of the response variable for this population are called the______, ______ and _____ respectively, corresponding to the specified value of the predictor variable.

In this Exercise 14.53, we repeat the information from Exercise 14.17.

a. Decide, at the 10%significance level, whether the data provide sufficient evidence to conclude that xis useful for predicting y:

b. Find a 90%confidence interval for the slope of the population regression line.

role="math" localid="1652352243033" x22344y34021 y^=5-x

In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether your can reasonably apply the conditional mean and predicted value t-interval procedures to the data. If so, then also do parts (b)-(h).
b. Determine and interpret a point estimate for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
c. Find and interpret a 95% confidence interval for the conditional mean of the response variable corresponding to the specified value of the predictor variable.
d. Determine and interpret the predicted value of the response variable corresponding to the specified value of the predictor variable.
e. Find and interpret a 95% prediction interval for the value of the response variable corresponding to the specified value of the predictor variable.
f. Compare and discuss the differences between the confidence interval that you obtained in part (c) and the prediction interval that you obtained in part (e).

14.101 Acreage and Value. The data from Exercise 14.37for lot size (in acres) and assessed value (in thousands of dollars) of a sample of homes in a particular area are on the WeissStats site. Specified value of the predictor variable: 2.5 acres.

In each of Exercises 14.64-14.69, apply Procedure 14.2 an page 567 to find and interpret a confidence interval, at the specified confidence level for the slope of the population regression line that relates rite response variable to the predicter variable.

Crown-Rump Length. Refer to Exercise 14.62;90%.

In this Exercise 14.54, we repeat the information from Exercise 14.18.

a. Decide, at the 10%significance level, whether the data provide sufficient evidence to conclude that xis useful for predicting y:

b. Find a 90%confidence interval for the slope of the population regression line.

role="math" localid="1652363608630" x1344y8031 y^=9-2x

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.

Sign-up for free