Correlation and Regression Project-2
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Jun 2, 2024
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MATH 110+11 – Elementary Statistics w/ Support Professor DeWilde Sara González
Correlation and Regression Project Due Date: Sunday, May 15, 2022 Part 1 - Correlation Table 1 - Simulation Results Trial
Correlation Guess
Actual Correlation
Description of Relationship
0.7
0.615
Strong, positive
2
0.7 0.556
moderate, positive
3
-0.3
-0.453
moderate, negative
4
0
-0.06
weak, negative
5
-0.86
-0.929
strong, negative
6
0.13
0.426
moderate, positive
7
0.87
0.687
moderate, positive
8
0.834
0.800
strong, positive
9
0.623
0.767
strong, positive
10
-0.753
-0.668
moderate, negative
1
MATH 110+11 – Elementary Statistics w/ Support Professor DeWilde Sara González
6.
Take a screenshot of the three graphs at the bottom of the screen that tracked your progress and insert your screenshot here. Note: Your graphs should contain 10 points that correspond to the guess and actual results that you obtained in your table above 7.
Looking back at your results, how do you think you did? How confident are you in your understanding of correlation? I think I did really well, considering I’ve never done this before! I feel pretty confident in my ability to gague the correlation. Part 2 – Regression For this part of the project, you will need to use the Rossman/Chance Least Squares Regression Applet
. You will be generating and interpreting the least-squares regression equation for a sample of data containing foot lengths and heights for a random sample of people. 1.
Using the context of foot lengths and heights, explain why the points in the given scatterplot do not lie on a perfectly straight line. There is a degree of variability in human growth— just because someone is 5’9” doesn’t mean their shoe size is automatically a 9. There could be taller people with small feet, and shorter people with big feet. However in general, the larger the person, the larger theit feet and the smaller the person, the smaller their feet. (
x
)
(
y
)
MATH 110+11 – Elementary Statistics w/ Support Professor DeWilde Sara González
2.
Click on “Show Movable Line” to generate a line in the scatterplot that can be moved by dragging the green squares around. Move these dots around to show a line that clearly does not fit the data. Take a screenshot of your scatterplot showing this line and insert it here. 3.
Now move the dots around to show a line that might fit the data. Take a screenshot of your scatterplot showing this line and insert it here.
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MATH 110+11 – Elementary Statistics w/ Support Professor DeWilde Sara González
4.
Click “Show Regression Line” to generate the least-squares regression line in your scatterplot. Take a screenshot showing both the scatterplot with the regression line and the equation of the regression line (shown just underneath the “Show Regression Line” option). 5.
What does it mean if an observation is above the least-squares regression line in the scatterplot? What does it mean if an observation is below the least-squares regression line in the scatterplot? If an observation is above the least-squares regression line, it means it has a value that is greater than what would be on the best line of fit, or like the average value for that particular dataset. Same thing for an observation below the least-squares regression line, it would have a value that is lesser than what would be the average for that particular data set. 6.
State and interpret the slope of the least-squares regression line. The slope of the least-squares regression line is 1.03. For each additional inch a person is tall, we expect their foot length to increase by 1.03 cm.
MATH 110+11 – Elementary Statistics w/ Support Professor DeWilde Sara González
7.
State and interpret (if possible) the -intercept of the least-squares regression line. The y-intercept of the least-squares regression line is 38.30. However, 0 is not a reasonable value for the explanatory variable, seeing as though someone cannot have a foot length of 0 cm. Therefore, the interpretation of the y-intercept line is worthless. 8.
Use the least-squares regression equation to predict the height of a person whose foot length is 28.5 cm, and show your work. y = 1.03x + 38.30 y = 1.03(28.5) + 38.30 y = 67.655 We would predict the height of a person whose foot length is 28.5 cm to be 67.655 inches. y