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Chapter 4: Q. 4.87 (page 181)

For regression analysis, 55T=8291.0and 5SR=7626.6.

a. Obtain and interpret the coefficient of determination.

b. Determine SSE :

Short Answer

Expert verified

a)

r2=0.92(92.0%)

Interpretation: Since the value obtained above is closer to 1 then evidently the variation in the observed variable is explained by the regression.

b)SSE=664.4

Step by step solution

01

Part (a) Step 1: Given Information

Given:

SSE=8291.0SSR=7626.6

02

Part (a) Step 2: Explanation

The coefficient of determination can be calculated as;

r2=SSRSSTr2=7626.68291.0r2=0.92(92.0%)

Interpretation: Since the value obtained above is closer to 1then evidently the variation in the observed variable is explained by the regression.

03

Part (b) Step 1: Given Information

To determine the value of SSE

04

Part (b) Step 2: Explanation

Given:

SST=8291.0SSR=7626.6

The Total Sum of Squares is equal to the Regression Sum of squares plus the error sum of squares.

That is,

localid="1650901802775" SST=SSR+SSESSE=SST-SSRSSE=8291.0-7626.6SSE=664.4

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Most popular questions from this chapter

Regarding linear equations with one independent variable, answer the following questions:
a. What is the general form of such an equation?
b. In your expression in part (a), which letters represent constants and which represent variables?
c. In your expression in part (a), which letter represents the independent variable and which represents the dependent variable?

As we noted, because of the regression identity, we can express the coefficient of determination in terms of the total sum of squares and the error sum of squares as r2=1-SSE/SST

a. Explain why this formula shows that the coefficient of determination can also be interpreted as the percentage reduction obtained in the total squared error by using the regression equation instead of the mean. Y炉. to predict the observed values of the response variable.

b.

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

What percentage reduction is obtained in the total squared error by using the regression equation instead of the mean of the observed prices to predict the observed prices?

In Exercise 4.7, we give linear equations. For each equation,

a. find the y-intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

given equation is,

y=-7x+6

In Exercise 4.8, we give linear equations. For each equation,

a. find the y-intercept and slope.

b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

c. use two points to graph the equation.

Given equation is,

y=-4x-8

More Money, More Beer? The data for per capita income and per capita beer consumption for the 50states and Washington, D.C., from Exercise 4.77 are on the WeissStats site.

a. decide whether the use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then also do parts (b) and (c).

b. obtain the linear correlation coefficient.

c. interpret the value of Xin terms of the linear relationship between the mo variables in question.
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