Statistics for Management and Economics
Statistics for Management and Economics
10th Edition
ISBN: 9781285425450
Author: Gerald Keller
Publisher: Cengage Learning
Question
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Chapter 16.6, Problem 101E

a:

To determine

Regression equation.

a:

Expert Solution
Check Mark

Explanation of Solution

The general regression equation can be written as follows:

y^=b0+b1x

The term y^ is the dependent variable (estimated value of the dependent value), the term b0 is the indicates intercept, the term x indicates the independent variable, and the term b1 indicates the coefficient of the independent variable.

Table 1 shows the processing of data as follows:

Table 1

Slxiyixi2yi2xi×yi
1-51525225-75
2-29481-18
3070490
43693618
544161616
6714917
Total742103408-52

Standard deviation (sxy) can be calculated as follows:

sxy=1n1[i=1nxiyii=1nxii=1nyin]=161[52(7)(426]=20.20

Standard deviation is -202.2.

The variance of x (sx2) can be calculated as follows:

sx2=1n1[i=1nxi2(i=1nxi)2n]=161[103(7)26]=18.97

The variance of x is 18.97.

The value of coefficient ( b1) can be calculated as follows:

b1=sxysx2=20.218.97=1.065

The value of b1 is -1.065.

The average value (x¯) of the independent variable x can be calculated as follows:

x¯=xin=76=1.167

The average value of x is 1.167.

The average value (y¯) of the independent variable x can be calculated as follows:

y¯=yin=426=7

The average value of x is 7.

Intercept b0 can be calculated as follows:

b0=y¯b1x¯=7(1.065)(1.167)=8.253

The intercept value is 8.253.

Thus, the regression equation is given below:

y^=8.2531.065x

b:

To determine

The predicted value of y.

b:

Expert Solution
Check Mark

Explanation of Solution

The estimated value of y (y^) can be calculated using the below equation:

y^=8.2531.065x

Table 2 shows the predicted value of x that is obtained using the regression equation with different levels of x values as follows:

Table 2

Slxiy^=8.2531.065x
1-513.58
2-210.38
308.253
435.058
543.993
670.758

c:

To determine

Calculate the residual.

c:

Expert Solution
Check Mark

Explanation of Solution

The value of residual (ei) can be calculated using the below equation:

ei=yiy^i        (1)

Table 3 shows the residual value that is obtained using Equation (1) as follows:

Table 3

Slxiy^=8.2531.065xei=yiy^i
1-513.581.42
2-210.38-1.38
308.253-1.253
435.0580.942
543.9930.007
670.7580.202

d:

To determine

Calculate the standardized residual.

d:

Expert Solution
Check Mark

Explanation of Solution

The variance of y (sy2) can be calculated as follows:

sy2=1n1[i=1nyi2(i=1nyi)2n]=161[408(42)26]=22.80

The variance of y is 22.8.

Error sum of square (SSE) can be calculated as follows:

SSE=(n1)(sy2sxy2sx2)=(61)(22.80(20.20)218.97)=6.451

Error sum of square is 6.451.

The value of sε can be calculated as follows:

sε=SSEn2=6.45162=1.270

The value of sε is 1.27.

The value of standardized residual (se) can be calculated using the below equation:

se=(eisε)        (2)

Table 5 shows the standardized residual value that is obtained using Equation (2) as follows:

Table 5

Slxiy^=8.2531.065xei=yiy^ise
1-513.581.421.18
2-210.38-1.38-1.087
308.253-1.253-0.987
435.0580.9420.742
543.9930.0070.0055
670.7580.2020.159

e:

To determine

Identification of outliers.

e:

Expert Solution
Check Mark

Explanation of Solution

From the above calculations, it is known that there are no outliers.

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Chapter 16 Solutions

Statistics for Management and Economics

Ch. 16.2 - Prob. 11ECh. 16.2 - Prob. 12ECh. 16.2 - Prob. 13ECh. 16.2 - Prob. 14ECh. 16.2 - Prob. 15ECh. 16.2 - Prob. 16ECh. 16.2 - Prob. 17ECh. 16.2 - Prob. 18ECh. 16.3 - Prob. 19ECh. 16.3 - Prob. 20ECh. 16.3 - Prob. 21ECh. 16.4 - Prob. 22ECh. 16.4 - Prob. 23ECh. 16.4 - Prob. 24ECh. 16.4 - Prob. 25ECh. 16.4 - Prob. 26ECh. 16.4 - Prob. 27ECh. 16.4 - Prob. 28ECh. 16.4 - Prob. 29ECh. 16.4 - Prob. 30ECh. 16.4 - Prob. 31ECh. 16.4 - Prob. 32ECh. 16.4 - Prob. 33ECh. 16.4 - Prob. 34ECh. 16.4 - Prob. 35ECh. 16.4 - Prob. 36ECh. 16.4 - Prob. 37ECh. 16.4 - Prob. 38ECh. 16.4 - Prob. 39ECh. 16.4 - Prob. 40ECh. 16.4 - Prob. 41ECh. 16.4 - Prob. 42ECh. 16.4 - Prob. 43ECh. 16.4 - Prob. 44ECh. 16.4 - Prob. 45ECh. 16.4 - Prob. 46ECh. 16.4 - Prob. 47ECh. 16.4 - Prob. 48ECh. 16.4 - Prob. 49ECh. 16.4 - Prob. 50ECh. 16.4 - Prob. 51ECh. 16.4 - Prob. 52ECh. 16.4 - Prob. 53ECh. 16.4 - Prob. 54ECh. 16.4 - Prob. 55ECh. 16.4 - Prob. 56ECh. 16.4 - Prob. 57ECh. 16.4 - Prob. 58ECh. 16.4 - Prob. 59ECh. 16.4 - Prob. 60ECh. 16.4 - Prob. 61ECh. 16.4 - Prob. 62ECh. 16.4 - Prob. 63ECh. 16.4 - Prob. 64ECh. 16.4 - Prob. 65ECh. 16.5 - Prob. 66ECh. 16.5 - Prob. 67ECh. 16.5 - Prob. 68ECh. 16.5 - Prob. 69ECh. 16.5 - Prob. 70ECh. 16.5 - Prob. 71ECh. 16.5 - Prob. 72ECh. 16.5 - Prob. 73ECh. 16.5 - Prob. 74ECh. 16.5 - Prob. 75ECh. 16.5 - Prob. 76ECh. 16.5 - Prob. 77ECh. 16.5 - Prob. 78ECh. 16.5 - Prob. 79ECh. 16.5 - Prob. 80ECh. 16.5 - Prob. 81ECh. 16.5 - Prob. 82ECh. 16.5 - Prob. 83ECh. 16.5 - Prob. 84ECh. 16.5 - Prob. 85ECh. 16.5 - Prob. 86ECh. 16.5 - Prob. 87ECh. 16.5 - Prob. 88ECh. 16.5 - Prob. 89ECh. 16.5 - Prob. 90ECh. 16.5 - Prob. 91ECh. 16.5 - Prob. 92ECh. 16.5 - Prob. 93ECh. 16.5 - Prob. 94ECh. 16.5 - Prob. 95ECh. 16.5 - Prob. 96ECh. 16.5 - Prob. 97ECh. 16.5 - Prob. 98ECh. 16.5 - Prob. 99ECh. 16.5 - Prob. 100ECh. 16.6 - Prob. 101ECh. 16.6 - Prob. 102ECh. 16.6 - Prob. 103ECh. 16.6 - Prob. 104ECh. 16.6 - Prob. 105ECh. 16.6 - Prob. 106ECh. 16.6 - Prob. 107ECh. 16.6 - Prob. 108ECh. 16.6 - Prob. 109ECh. 16.6 - Prob. 110ECh. 16.6 - Prob. 111ECh. 16.6 - Prob. 112ECh. 16.6 - Prob. 113ECh. 16.6 - Prob. 114ECh. 16.6 - Prob. 115ECh. 16.6 - Prob. 116ECh. 16.6 - Prob. 117ECh. 16.6 - Prob. 118ECh. 16.A - Prob. 1ECh. 16.A - Prob. 2ECh. 16.A - Prob. 3ECh. 16.A - Prob. 4ECh. 16.A - Prob. 5ECh. 16.A - Prob. 6ECh. 16.A - Prob. 7ECh. 16.A - Prob. 8ECh. 16.A - Prob. 9ECh. 16.A - Prob. 10ECh. 16.A - Prob. 11ECh. 16.A - Prob. 12ECh. 16.A - Prob. 13ECh. 16.A - Prob. 14ECh. 16.A - Prob. 15ECh. 16.A - Prob. 16ECh. 16 - Prob. 119CECh. 16 - Prob. 120CECh. 16 - Prob. 121CECh. 16 - Prob. 122CECh. 16 - Prob. 123CECh. 16 - Prob. 124CECh. 16 - Prob. 125CECh. 16 - Prob. 126CECh. 16 - Prob. 127CECh. 16 - Prob. 128CECh. 16 - Prob. 129CE
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