Complete the following objectives for each data set: (a) Calculate the coefficient of determination, r2.(b) Interpret the meaning of r2 for the given set of data. (c) Find the equation of the least-squares regression line, if appropriate. Many universities use a student’s ACT score to help with admission decisions as well as placement decisions. From a sample of 20 students, the following data are obtained. ACT Score College GPA 16 1.85 18 2.20 24 2.80 25 3.50 34 4.00 27 3.18 29 3.90 25 2.90 30 4.00 21 2.60 17 2.50 21 3.65 28 3.10 31 3.72 35 3.24 18 2.30 17 1.70 26 3.10 28 3.50 23 2.76
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.
Complete the following objectives for each data set:
(a) Calculate the coefficient of determination, r2.
(b) Interpret the meaning of r2 for the given set of data.
(c) Find the equation of the least-squares regression line, if appropriate.
Many universities use a student’s ACT score to help with admission decisions as well as placement decisions. From a sample of 20 students, the following data are obtained.
|
ACT Score |
College GPA |
|
16 |
1.85 |
|
18 |
2.20 |
|
24 |
2.80 |
|
25 |
3.50 |
|
34 |
4.00 |
|
27 |
3.18 |
|
29 |
3.90 |
|
25 |
2.90 |
|
30 |
4.00 |
|
21 |
2.60 |
|
17 |
2.50 |
|
21 |
3.65 |
|
28 |
3.10 |
|
31 |
3.72 |
|
35 |
3.24 |
|
18 |
2.30 |
|
17 |
1.70 |
|
26 |
3.10 |
|
28 |
3.50 |
|
23 |
2.76 |
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
