.Week 7 – Linear Regression and Correlation
38636. Given the following
Book Pages (x variable) Price (y variable)
A 250 $8.25
B 364 $10.00
C 245 $8.00
D 399 $11.00
E 374 $10.75
F 340 $9.25
G 357 $9.75
.
Create a scatter diagram which shows the trendline (this is the regression line) and provides the coefficient of determination on the graph itself. Include your Excel sheet in your submission. (Upload it)
b. What is the equation of the trendline from the graph? (Just copy it from your graph)
c. According to the equation of the trendline from your graph, if a book had 200 pages, how much should it cost?
d. According to the equation of the trendline from your graph, if a book costs $10.15, how many pages should it have?
e. In part c and d, were you interpolating or extrapolating? How do you know? How confident are you that the number of pages would really be what you calculated it to be? Why?
f. Given the r value of the trendline, describe the strength of the relationship between pages and price. Should we be using this trendline to interpolate? Extrapolate?
g. When considering interpolation, extrapolation, and r values – how should we put these concepts together to come up with an idea of how confident we are to use a trendline in a business situation?
2. The axes labels and title have intentionally been removed from this scatter diagram which shows the trendline.
Review the following scatter diagram.
True or false? Justify your answer by writing a sentence or two after each one.
a. It is possible that r = 1
b. The slope of the line will be negative.
c. The value of r is extremely close to -1.
e. There is a very strong correlation between the two variables (whatever they might be) on this graph.
f. It is safe to use this trendline as the only factor considered in a business decision.
g. A trendline is the line of best fit for a data set.
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