MA215 Grantham Wk 7 Scatter Diagram & Coefficient of Determination Paper

User Generated

yvivr34

Mathematics

MA215

Grantham University

Description

Question 1


Assume you have noted the following prices for paperback books and the number of pages that each book contains.

Book

Pages (x variable)

Price (y variable)

A

500

$7.00

B

610

$8.25

C

550

$7.30

D

650

$8.45

E

530

$7.25

F

600

$8.00

G

477

$6.25

  1. Create a scatter diagram using Excel for the data in the above chart. Place the trendline, the equation of the trendline, and the coefficient of determination on the scatter diagram. Hint from Dr. Klotz: The trendline can be added by using the green + sign that appears right after making the graph. Click on the + and go down to trendline. There is a black triangle next to the word "trendline" - use that to get the equation and coefficient of determination on the graph.
  2. Define "coefficient of determination" and "Pearson's product moment correlation coefficient." Explain the relationship between the coefficient of determination and Pearson's product moment correlation coefficient. What does each one tell us?
  3. Compute the value for Pearson's product moment correlation coefficient. What does it tell us about the strength of the relationship between the x and y variables?
  4. According to the equation for the trendline, if there are 640 pages in the book, how much should it cost?
  5. According to the trendline, if the cost of the book were $12.25, how many pages should there be?
  6. Why would some hesitate to accept the answer in #5 but not hesitate to accept the answer in #4?
  7. Conduct a full hypothesis test to see if x and y are related. Use α = 0.05.

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Explanation & Answer

Please find attached the complete work.

1.

SCATTER DIAGRAM
The trendline, the equation of the trendline, and the coefficient of determination are on the
scatter diagram
$9.00
y = 0.0121x + 0.738
R² = 0.9529

$8.50

Price,y

$8.00
$7.50
$7.00
$6.50
$6.00
400

450

500

550

600

650

700

No of pages,x

2.
The coefficient of determination tells us about how fit a model is for the given statistical data. It
indicates the explained variability in the data set.
For a linear regression model having one independent variable the coefficient of determination is:

R 2 = (1 / N )   [( xi − x )  ( y i − y ) /( x   y ) 2
N = Number of observatio n
x i = x value of observatio n i
y i = y value of observatio n i
x = mean value of x
y = mean value of y
 x = Standard deviation of x

 y = S...


Anonymous
Just what I was looking for! Super helpful.

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