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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.

Short Answer

Expert verified

Conditional distribution, conditional mean, and standard deviation,

Step by step solution

01

Given information

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.

02

Explanation

The population's conditional distribution is defined as the distribution of the response variable.

The standard deviation is called the conditional standard deviation, and the mean is called the conditional mean.

"The distribution, mean, and standard deviation of the response variable for this population are called the conditional distribution, conditional mean, and standard deviation, respectively, corresponding to the specified value of the predictor value.

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Most popular questions from this chapter

In Exercises 14.48-14.57, we repeat the information from Exercises 14.12-14.21.

a. Decide, at the lore significance level, whether the data provide sufficient evidence to conclude that \(x\) is useful for predicting y.

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

y=2.875-0.625x

In Exercises 14.98-14.108, use the technology of your choice to do the following tasks.
a. Decide whether you 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% Te 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 a95% 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).
14.100 Movie Grosses. The data from Exercise 14.36 on domestic and overseas grosses for a random sample of 50 movies are on the WeissStats site. Specified value of the predictor variable: S 100 million.

Following are the data on age of fetuses and length of crown-rump.useฮฑ=0.10presuming that the assumption for regression inference are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for providing the response variable.

we repeat the data and provide the sample regression equations for Exercises a.Determine the standard error of the estimate.

b. Construct a residual plot.

c. Construct a normal probability plot of the residuals.

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%Te 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).

14.10 PCBs and Pelicans. The data from Exercise 14.40for shell thickness and concentration of PCBs of 60Anacapa pelican eggs are on the WeissStats site. Specified value of the predictor variable: 220ppm.

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