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Chapter 14: 14.31 (page 562)

Plant Emissions. Use the data on plant weight and quantity of volatile emissions from Exercise 14.25.

a. compute the standard error of the estimate and interpret your answer

b. interpret your result from part (a) if the assumptions for regression inferences hold.

c. obtain a residual plot and a normal probability plot of the residuals.

d. decide whether you can reasonably consider Assumptionsfor regression inferences to be met by the variables under consideration. (The answer here is subjective, especially in view of the extremely small sample sizes.)

Short Answer

Expert verified

a). The required solution is 1.64.

b). The predicted value will differ by 1.64from the actual value.

c). The residual plot and normal probability plot shown below.

d). The residual plot shows no pattern, and the normal probability plot is linear, so it seems reasonable.

Step by step solution

01

Part (a) Step 1: Given Information

Given data:

02

Part (a) Step 2: Explanation

Using the above data, calculate the standard deviation.

蟽=鈭�xi-渭2N

We will obtain after solving

蟽=5.447

The standard error is then calculated.

Standard error蟽e=蟽n 蟽e=5.44711

=1.64

03

Part (b) Step 1: Given Information

Given data:

04

Part (b) Step 2: Explanation

As may be seen in part (a), the standard error is about

Standard error 蟽e=蟽n

蟽e=5.44711

=1.64

As a result, the predicted value will differ 1.64 from the actual value.

05

Part (c) Step 1: Given Information

Given data:

06

Part (c) Step 2: Explanation

Determine the residual.

residual=y-y^

Here y^is the linear fit value.

Create a residual plot and a normal probability plot in MATLAB.

Residual plot:

Normal probability plot:

07

Part (d) Step 1: Given Information

Given data:

08

Part (d) Step 2: Explanation

The residual plot shows no pattern, and the normal probability plot is linear, so it seems reasonable.

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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.

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

14.95 Plant Emissions. Following are the data on plant weight and quantity of volatile emissions from Exercise 14.25.

x
57
85
57
65
52
67
62
80
77
53
68
y
8.0
22.0
10.5
22.5
12.0
11.5
7.5
13.0
16.5
21.0
12.0

a. Obtain a point estimate for the mean quantity of volatile emissions of all (Solanum tuberosum) plants that weigh 60g.
b. Find a 95%confidence interval for the mean quantity of volatile emissions of all plants that weigh 60g.
c. Find the predicted quantity of volatile emissions for a plant that weighs 60g.
d. Determine a 95%prediction interval for the quantity of volatile emissions for a plant that weighs 60g.

Following are the age and price data for custom homes, use 伪=0.01

presuming 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.

14.7 The difference between an observed value and a predicted value of the response variable is called a________
See all solutions

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