1) You compare the height and weight of 5 adult women. You get the following results: height 60 67 62 70 66 weight 119 143 131 155 136 (a) Construct a scatter plot of height (x) vs. weight (v) (b) Calculate the following (show your work for SS.p): SS. S, SS.p (c) Calculate the correlation coefficient (r)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![Do NOT use R for problems 1-4:
1) You compare the height and weight of 5 adult women. You get the following results:
height
60
67
62
70
66
weight
119
143
131
155
136
(a) Construct a scatter plot of height (x) vs. weight (v)
(b) Calculate the following (show your work for SS.p):
SS.
S,
SSep
(c) Calculate the correlation coefficient (r)
2) Use the information from problem 1. Perform a complete test of the hypothesis that the population
correlation coefficient (p) is 0. Show all steps (note - obviously this should be a one sided test! Make sure you
know why!).
3) Now let's assume you wanted to predict weights from heights. In other words, now let's use the same data
from problem (1) and do a regression instead.
(a) Calculate bo and b.
(b) Carefully draw your least square regression line on the plot you made in 1(a). (Don't just "sketch",
be a little careful).
4) (a) Now do a significance test of Ho: B1 = 0. Show all your calculations (including your residual
calculations). Again, note that this should be a one sided test (why?).
(b) Compare your t from 4(a) with your f from problem 2. Are they the same? This is not a coincidence,
although once you do more complicated analyses, you can't rely on this "equivalence".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89c0aec8-fa87-403f-a89a-bd303d48e75d%2Fd0209246-db9e-478b-bc6e-6ad39e9fe888%2Fhd9mxoc_processed.jpeg&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![MATLAB: An Introduction with Applications](https://www.bartleby.com/isbn_cover_images/9781119256830/9781119256830_smallCoverImage.gif)
![Probability and Statistics for Engineering and th…](https://www.bartleby.com/isbn_cover_images/9781305251809/9781305251809_smallCoverImage.gif)
![Statistics for The Behavioral Sciences (MindTap C…](https://www.bartleby.com/isbn_cover_images/9781305504912/9781305504912_smallCoverImage.gif)
![Elementary Statistics: Picturing the World (7th E…](https://www.bartleby.com/isbn_cover_images/9780134683416/9780134683416_smallCoverImage.gif)
![The Basic Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319042578/9781319042578_smallCoverImage.gif)
![Introduction to the Practice of Statistics](https://www.bartleby.com/isbn_cover_images/9781319013387/9781319013387_smallCoverImage.gif)