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The basket ball coach at a small local college believes that his team plays better and scores more points in front of larger crowds. The number of points scored and attendance for all home games last season are reported here. Do these data support the coach’s argument? Game Point scored Attendance 1 54 378 2 57 350 3 59 320 4 80 478 5 82 451 6 75 250 7 73 489 8 53 451 9 67 410 10 78 215 11 67 113 12 56 250 13 85 450 14 101 489 15 99 472

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Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

Solutions

Chapter
Section
BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 12, Problem 12.5P
Textbook Problem
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The basket ball coach at a small local college believes that his team plays better and scores more points in front of larger crowds. The number of points scored and attendance for all home games last season are reported here. Do these data support the coach’s argument?

Game Point scored Attendance
1 54 378
2 57 350
3 59 320
4 80 478
5 82 451
6 75 250
7 73 489
8 53 451
9 67 410
10 78 215
11 67 113
12 56 250
13 85 450
14 101 489
15 99 472

To determine

To show:

The given data supports coach’s argument.

Explanation of Solution

Given:

The given statement is,

The number of points scored and attendance for all home games last season are reported.

The given table of information is,

Game Point scored Attendance
1 54 378
2 57 350
3 59 320
4 80 478
5 82 451
6 75 250
7 73 489
8 53 451
9 67 410
10 78 215
11 67 113
12 56 250
13 85 450
14 101 489
15 99 472

Approach:

The Y intercept (a) is the point of intersection of the regression line and the y axis.

The slope (b) of the regression line is the amount of change in the dependent variable (Y) by a unit change in the independent variable (X).

If the two variables are unrelated, the regression line would be parallel to the x axis.

Formula used:

The model for the least square regression line is defined as,

Y=a+bX

Where Y is the dependent variable,

X is the independent variable,

a is the Y intercept of the regression line

and, b is the slope of the regression line.

The formula for calculating the correlation coefficient r is given as,

r=(XX¯)(YY¯)[(XX¯)2][(YY¯)2]

Where X and Y are the two variables

And X¯ and Y¯ are their respective means.

Calculation:

From the given information,

The Point scored is the dependent variable. Thus, it is represented as Y.

The Attendance is the independent variables. Thus, it is as X.

Consider the following table of sum of squares of democrat and voter turnout.

Case Attendance (X) (XX¯) (XX¯)2 Point scored (Y) (YY¯) (YY¯)2 (XX¯)(YY¯)
1 378 6.933 48.0665 54 18.4 338.56 127.57
2 350 21.067 443.818 57 15.4 237.16 324.432
3 320 51.067 2607.84 59 13.4 179.56 684.298
4 478 106.933 11434.7 80 7.6 57.76 812.691
5 451 79.933 6389.28 82 9.6 92.16 767.357
6 250 121.07 14657.2 75 2.6 6.76 314.77
7 489 117.933 13908.2 73 0.6 0.36 70.7598
8 451 79.933 6389.28 53 19.4 376.36 1550.7
9 410 38.933 1515.78 67 5.4 29.16 210.24
10 215 156.07 24356.9 78 5.6 31.36 873.98
11 113 258.07 66598.6 67 5.4 29.16 1393.56
12 250 121.07 14657

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