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Chapter 14: Q. 14.2 (page 560)

State the four conditions required for making regression inferences.

Short Answer

Expert verified

1. Independent observations

2. Equal standard deviations

3. Normal populations

4. Population regression line.

Step by step solution

01

Given information

The four conditions required for making regression inferences

02

Explanation

The following are the requirements for making regression inferences:

1. Independent observations: The responses to variable observations are unrelated to one another.

2. Equal standard deviations: The conditional standard deviations of the response variable are the same for all values of the predictor variable.

3. Normal populations: For each value of the predictor variable, the conditional distribution of the responder variable is a normal distribution.

4. Population regression line: There are constants β0and β1such that the conditional mean of the response variables is β0+β1xfor each value of x for the predictor variable.

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Most popular questions from this chapter

In this Exercise 14.52, we repeat the information from Exercise 14.16.

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.

x1344y13-135 y^=14-3x

In this Exercise 14.51, we repeat the information from Exercise 14.15.

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="1652333468446" x3412y450-1 role="math" localid="1652333507650" y^=-3+x

14.93 Corvette Prices. Following are the age and price data for Corvettes from Exercise 14.23.

x
6
6
6
2
2
5
4
5
1
4
y
290
280
295
425
384
315
355
328
425
325

a. Obtain a point estimate for the mean price of all 4-year-old Corvettes.

b. Determine a 90% confidence interval for the mean price of all 4-year-old Corvettes.

c. Find the predicted price of a 4-year-old Corvette.
d. Determine a 90% prediction interval for the price of a 4 -year-old Corvette.
e. Draw graphs similar to those in Fig. 14.11 on page 576 , showing
f. Why is the prediction interval wider than the confidence interval?

Corvette Prices. The Kelley Blue Book provides information on wholesale and retail prices of cars. Following are age and price data for 10randomly selected Corvettes between 1and 6years old.

Here, xdenotes age, in years, and ydenotes price, in hundreds of dollars.

Which graph used in a residual analysis provides roughly the same information as a scatterplot? What advantages does it have over a scatterplot?
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