Question

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.

Answer 1

1)

--. (best line) Series 1 meta-chart,com

Take x on the horizontal axis and y on the vertical axis. Plot the different combinations of x,y to get the scatterplot.

The regression line is given as: Y = A + Bx

From the data, B = Sxy/Sxx , A = ybar - Bxbar

From the data, ybar = 7.6143 , xbar = 559.5714

Sxx = $\sum$x^2 -( $\sum$x)^2/n = 2215529 - 3917^2/7 = 23687.7143

Sxy = $\sum$xy - $\sum$x$\sum$y/n = 30173.75 - 3917*53.3/7 = 348.5929

So, B= 0.0147 and A = -0.6205

So the regression line is Y= -0.6205 + 0.0147x

2)

The coefficient of determination (denoted by R²) is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.

The coefficient of determination is the square of the correlation (r) between predicted y scores and actual y scores; thus, it ranges from 0 to 1.

With linear regression, the coefficient of determination is also equal to the square of the correlation between x and y scores.

An R² of 0 means that the dependent variable cannot be predicted from the independent variable.

An R² of 1 means the dependent variable can be predicted without error from the independent variable.

A statistic measuring the linear relationship between two variables in a sample and used as an estimate of the correlation in the whole population.

The most commonly used method of computing a correlation coefficient between variables that are linearly related.

In simple terms, Correlation Coefficient shows the extent of “linear” relationship between two variables. Whereas Coefficient of Determination is a measure of goodness of fit for the model under study, i.e. it shows how much variation is explained by the model with respect to the total variation present in the data set.

3)

Coefficient of determination= r^2

Where, r= Sxy/√Sxx*Syy = 0.98165

So r^2 = 0.96363

So 96.36% of variation in price is explained by the no of pages of a book.

Pearson correlation coefficient r =

Sp (r -*(y)

=

348.5929 /229.5714 7.6143

= 0.9816

4)

According to the equation for the trend line, if there are 640 pages in the book cost is

Y= -0.6205 + 0.0147x

Y= -0.6205 + 0.0147(640)

Y= $ 8.7875

According to the equation for the trend line, if there are 640 pages in the book cost is $ 8.7875.

As per HomeworkLib policy we need to solve four sub parts per question. Please post the remaining questions in another post.