PRACTICE OF STATISTICS F/AP EXAM
PRACTICE OF STATISTICS F/AP EXAM
6th Edition
ISBN: 9781319113339
Author: Starnes
Publisher: MAC HIGHER
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Chapter 12.2, Problem 50E

(a)

To determine

To construct: an appropriate scatter plot predicting click through rate from position.

(a)

Expert Solution
Check Mark

Answer to Problem 50E

There is negative, strong, curved relation between position and click through rate.

Explanation of Solution

Given:

    PositionClick through rate
    123.53
    214.94
    311.19
    47.47
    55.29
    63.8
    72.79
    82.11
    91.57
    101.18

Graph:

Scatter plot

  PRACTICE OF STATISTICS F/AP EXAM, Chapter 12.2, Problem 50E , additional homework tip  1

Form: curved, the reason is that the points are not lying on the straight line

Direction: Negative, the reason is that the pattern is downwards in the scatter plot.

Strength: strong, the reason is that all points lie don’t deviate much from the general pattern in the points.

(b)

To determine

To Explain: that this relationship follows an exponential model or a power model.

(b)

Expert Solution
Check Mark

Answer to Problem 50E

Exponential Model

Explanation of Solution

Given:

    PositionClick through rate
    123.53
    214.94
    311.19
    47.47
    55.29
    63.8
    72.79
    82.11
    91.57
    101.18

Graph:

  PRACTICE OF STATISTICS F/AP EXAM, Chapter 12.2, Problem 50E , additional homework tip  2

  PRACTICE OF STATISTICS F/AP EXAM, Chapter 12.2, Problem 50E , additional homework tip  3

The scatter plot of position v/s log (click through rate) represent no strong curved, that means that an exponential model would be appropriate.

(c)

To determine

To Explain: the equation of the regression line.

(c)

Expert Solution
Check Mark

Answer to Problem 50E

  lny=1.46740.1430lnx

Explanation of Solution

Given:

    PositionClick through rate
    123.53
    214.94
    311.19
    47.47
    55.29
    63.8
    72.79
    82.11
    91.57
    101.18

Formula used:

  a=y.x2xxynx2(x)2b=nxyx.ynx2(x)2y=a+b.x

Calculation:

X is the logarithm of length and Y is the logarithm of heart weight

    PositionClick through rateXYXYX2
    123.5303.15827620300
    214.940.6931471812.704042181.8742992130.480453
    311.191.0986122892.4150205222.6531712231.206949
    47.471.3862943612.0108949992.7876923981.921812
    55.291.6094379121.6658182462.681031042.59029
    63.81.7917594691.3350010672.3920008033.210402
    72.791.9459101491.0260415961.9965847553.786566
    82.112.0794415420.7466879471.5526939374.324077
    91.572.1972245770.4510756190.9911144374.827796
    101.182.3025850930.1655144380.3811110795.301898
    x=15.10441257y =15.67837282xy =17.30969888x2 =27.65024
    XYX2
    00

Using from the table find the value of a and b

  a=y.x2xxynx2(x)2 =1.4674

  b=nxyx.ynx2(x)2 =-0.1430

Substituting the value of a and b in the regression equation formula

  y=a+b.xy=1.46740.1430x

The least squares regression equation

  lny=1.46740.1430lnx

Where x is the position and y the click through rate

(d)

To determine

To Explain: the prediction from the part (c) of the click through rate for a website in the 11th position.

(d)

Expert Solution
Check Mark

Answer to Problem 50E

0.784152%

Explanation of Solution

Given:

    PositionClick through rate
    123.53
    214.94
    311.19
    47.47
    55.29
    63.8
    72.79
    82.11
    91.57
    101.18

Calculation:

Using the part (c)

  lny=1.46740.1430lnx

Putting the value of x

  lny=1.46740.1430lnxlny=1.46740.1430ln(11)lny=0.1056

Taking the exponential

  y=elogy=e0.1056=0.784152

Therefore the expected click through rate is 0.784152%

Chapter 12 Solutions

PRACTICE OF STATISTICS F/AP EXAM

Ch. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - Prob. 50ECh. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12 - Prob. R12.1RECh. 12 - Prob. R12.2RECh. 12 - Prob. R12.3RECh. 12 - Prob. R12.4RECh. 12 - Prob. R12.5RECh. 12 - Prob. R12.6RECh. 12 - Prob. T12.1SPTCh. 12 - Prob. T12.2SPTCh. 12 - Prob. T12.3SPTCh. 12 - Prob. T12.4SPTCh. 12 - Prob. T12.5SPTCh. 12 - Prob. T12.6SPTCh. 12 - Prob. T12.7SPTCh. 12 - Prob. T12.8SPTCh. 12 - Prob. T12.9SPTCh. 12 - Prob. T12.10SPTCh. 12 - Prob. T12.11SPTCh. 12 - Prob. T12.12SPTCh. 12 - Prob. AP4.1CPTCh. 12 - Prob. AP4.2CPTCh. 12 - Prob. AP4.3CPTCh. 12 - Prob. AP4.4CPTCh. 12 - Prob. AP4.5CPTCh. 12 - Prob. AP4.6CPTCh. 12 - Prob. AP4.7CPTCh. 12 - Prob. AP4.8CPTCh. 12 - Prob. AP4.9CPTCh. 12 - Prob. AP4.10CPTCh. 12 - Prob. AP4.11CPTCh. 12 - Prob. AP4.12CPTCh. 12 - Prob. AP4.13CPTCh. 12 - Prob. AP4.14CPTCh. 12 - Prob. AP4.15CPTCh. 12 - Prob. AP4.16CPTCh. 12 - Prob. AP4.17CPTCh. 12 - Prob. AP4.18CPTCh. 12 - Prob. AP4.19CPTCh. 12 - Prob. AP4.20CPTCh. 12 - Prob. AP4.21CPTCh. 12 - Prob. AP4.22CPTCh. 12 - Prob. AP4.23CPTCh. 12 - Prob. AP4.24CPTCh. 12 - Prob. AP4.25CPTCh. 12 - Prob. AP4.26CPTCh. 12 - Prob. AP4.27CPTCh. 12 - Prob. AP4.28CPTCh. 12 - Prob. AP4.29CPTCh. 12 - Prob. AP4.30CPTCh. 12 - Prob. AP4.31CPTCh. 12 - Prob. AP4.32CPTCh. 12 - Prob. AP4.33CPTCh. 12 - Prob. AP4.34CPTCh. 12 - Prob. AP4.35CPTCh. 12 - Prob. AP4.36CPTCh. 12 - Prob. AP4.37CPTCh. 12 - Prob. AP4.38CPTCh. 12 - Prob. AP4.39CPTCh. 12 - Prob. AP4.40CPTCh. 12 - Prob. AP4.41CPTCh. 12 - Prob. AP4.42CPTCh. 12 - Prob. AP4.43CPTCh. 12 - Prob. AP4.44CPTCh. 12 - Prob. AP4.45CPTCh. 12 - Prob. AP4.46CPT
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