EBK STATISTICS FOR MANAGEMENT AND ECONO
EBK STATISTICS FOR MANAGEMENT AND ECONO
11th Edition
ISBN: 9781337516723
Author: KELLER
Publisher: YUZU
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Chapter 4.4, Problem 85E

(a)

To determine

Determine the covariance and coefficient of correlation.

(a)

Expert Solution
Check Mark

Explanation of Solution

Covariance is a measure that is used to measure the relationship between the movements of two variables. Thus, covariance measures how changes in one variable are associated with the changes in a second variable. Therefore, covariance measures the degree to which two variables are linearly associated. In this case, covariance can be measured after calculating the square of x and y and the product of xy as follows:

xiyixi2yi2xiyi
2014400196280
40161600256640
601836003241080
50172500289850
50182500324900
55183025324990
601836003241080
702049004001400
i=1nxi=405i=1nyi=139i=1nxi2=22,125i=1nyi2=2,437i=1nxiyi=7,220

Covariance can be calculated as follows:

sxy=1n1[i=1nxiyii=1nxii=1nyin]=181[7,220(405)(139)8]=26.16

The values of two standard deviations can be calculated as follows:

sx2=1n1[i=1nxi2(i=1nxi)2n]=181[22,125(405)28]=231.7

sx=sx2=231.7=15.22

Similarly,

sy2=1n1[i=1nyi2(i=1nyi)2n]=181[2,437(139)28]=3.13

sy=sy2=3.13=1.77

Coefficient of correlation=CovariancexyStandard deviationxStandard deviationy=SxySxSy=26.16(15.22)(1.77)=26.1626.9394=0.97106

The coefficient of determination can be calculated by squaring the coefficient of correlation as follows:

Coefficient of determination=(Coefficient of correlation)2=(0.9711)2=0.9430

Thus, covariance is calculated to be 26.16 and the coefficient of correlation is calculated to be 0.9711. The coefficient of determination is also calculated, and it is 0.9430. These values indicate that 94.30 percent of variation in variable ‘y’ is explained by the variations in variable ‘x’.

Economics Concept Introduction

Covariance: Covariance is a measure that is used to measure the relationship between the movements of two variables.

(b)

To determine

Determine the least squares line and estimate the retailer wants.

(b)

Expert Solution
Check Mark

Explanation of Solution

Covariance is calculated to be 26.16, and the value of S2x is 231.7. Thus, the value of b1 can be calculated as follows:

b1=SxyS2x=26.16231.7=0.113

The values of X¯ and Y¯ can be calculated as follows:

X¯=Xin=4058=50.63

Similarly,

Y¯=Yin=1398=17.38

The value of b0 can be calculated as follows:

b0=Y¯b1X¯=17.38(0.113×50.63)=11.66

The least square line will thus be y^=11.66+0.113x. This means that the estimated variable cost is 0.113 and the estimated fixed cost is 11.66.

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Chapter 4 Solutions

EBK STATISTICS FOR MANAGEMENT AND ECONO

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - Prob. 72ECh. 4.3 - Prob. 73ECh. 4.3 - Prob. 74ECh. 4.3 - Prob. 75ECh. 4.3 - Prob. 76ECh. 4.3 - Prob. 77ECh. 4.3 - Prob. 78ECh. 4.3 - Prob. 79ECh. 4.3 - Prob. 80ECh. 4.3 - Prob. 81ECh. 4.3 - Prob. 82ECh. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4.4 - Prob. 88ECh. 4.4 - Prob. 89ECh. 4.4 - Prob. 90ECh. 4.4 - Prob. 91ECh. 4.4 - Prob. 92ECh. 4.4 - Prob. 93ECh. 4.4 - Prob. 94ECh. 4.4 - Prob. 95ECh. 4.4 - Prob. 96ECh. 4.4 - Prob. 97ECh. 4.4 - Prob. 98ECh. 4.4 - Prob. 99ECh. 4.4 - Prob. 100ECh. 4.4 - Prob. 101ECh. 4.4 - Prob. 102ECh. 4.4 - Prob. 103ECh. 4.4 - Prob. 104ECh. 4.4 - Xr04-105 The number of wins, team payrolls, home...Ch. 4.4 - Prob. 106ECh. 4.4 - Prob. 107ECh. 4.4 - Prob. 108ECh. 4.4 - Prob. 109ECh. 4.4 - Prob. 110ECh. 4.5 - Prob. 111ECh. 4.5 - Prob. 112ECh. 4.5 - Prob. 113ECh. 4.5 - Prob. 114ECh. 4.5 - Prob. 115ECh. 4.5 - Prob. 116ECh. 4.5 - Prob. 117ECh. 4.5 - Prob. 118ECh. 4.5 - Prob. 119ECh. 4.5 - Prob. 120ECh. 4.5 - Prob. 121ECh. 4.5 - Prob. 122ECh. 4.5 - Prob. 123ECh. 4.5 - Prob. 124ECh. 4.5 - Prob. 125ECh. 4.5 - Prob. 126ECh. 4.5 - Prob. 127ECh. 4.5 - Prob. 128ECh. 4.5 - Prob. 129ECh. 4.5 - Prob. 130ECh. 4.5 - Prob. 131ECh. 4.6 - Prob. 132ECh. 4.6 - Prob. 133ECh. 4.6 - Prob. 134ECh. 4.6 - Prob. 135ECh. 4.6 - Prob. 136ECh. 4.6 - Prob. 137ECh. 4.6 - Prob. 138ECh. 4 - Prob. 139CECh. 4 - Prob. 140CECh. 4 - Prob. 141CECh. 4 - Prob. 142CECh. 4 - Prob. 143CECh. 4 - Prob. 144CECh. 4 - Prob. 145CECh. 4 - Prob. 146CECh. 4 - Prob. 147CECh. 4 - Prob. 148CECh. 4 - Prob. 149CECh. 4 - Prob. 150CECh. 4 - Prob. 151CECh. 4 - Prob. 152CECh. 4 - Prob. 153CECh. 4 - Prob. 154CE
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