Statistics for Management and Economics
Statistics for Management and Economics
10th Edition
ISBN: 9781285425450
Author: Gerald Keller
Publisher: Cengage Learning
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Chapter 16, Problem 119CE

a:

To determine

Calculate the coefficient.

a:

Expert Solution
Check Mark

Explanation of Solution

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

b1=sxysx2=74.023.47=21.33

The value of coefficient is 21.33.

The intercept (b0) value can be calculated as follows:

b0=y¯b1x¯= 384.8121.33(4.12)=296.93

The value of intercept is 296.93.

The general regression equation can be written as follows:

y^=b0+b1x

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

Thus, the sample regression equation can be written as follows:

y^=296.93+21.33x

b:

To determine

Interpretation.

b:

Expert Solution
Check Mark

Explanation of Solution

The coefficient indicates that increasing one unit of independent variable (advertisement) leads to increase in the dependent variable (customer) by 21.33.

c:

To determine

Testing the hypothesis.

c:

Expert Solution
Check Mark

Explanation of Solution

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

SSE=(n1)(sy2sxy2sx2)=(261)(18,552(74.02)23.47)=424,326

Error sum of square is 424,326.

The value of sε can be calculated as follows:

sε=SSEn2=424,326262=132.97

The value of sε is 132.97.

Null hypothesis (H0) is β1=0 and alternate hypothesis (H1) β1>0.

The t table value can be calculated as follows:

t>tα,n2=t0.05,502=1.711

The t table value is 1.711.

The value of sb1 can be calculated as follows:

sb1=sε(n1)sx2=132.97(261)(3.47)=14.28

The value of sb1 is 14.28.

Calculated t-value can be obtained as follows:

t=b1β1sb1=21.33014.28=1.49

The t-value is 1.49. Since the calculated t-value is less than the t table value, the alternate hypothesis is not accepted.

d:

To determine

Coefficient of determination.

d:

Expert Solution
Check Mark

Explanation of Solution

Coefficient of determination i (R2) can be calculated as follows:

R2=sxy2sx2sy2=(74.02)2(3.47)(18,552)=0.0851

The coefficient for the determination is 0.0851. The R2 value indicates that a weak linear relationship exists between the independent variable and dependent variable.

e:

To determine

Interpretation.

e:

Expert Solution
Check Mark

Explanation of Solution

Since the model reveals that a weak relationship exists between the independent and dependent variables, the prediction would not be accurate.

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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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