In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam
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.
In order for applicants to work for the foreign-service department, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that applicants have studied a particular language and the grades they received on the proficiency exam.
| Number of years, x | 4 | 3 | 4 | 5 | 3 | 6 | 2 | 7 | 3 |
| Grades on the proficiency exam, y | 62 | 66 | 76 | 84 | 73 | 90 | 61 | 96 | 72 |
(d) Predict the grade an applicant will receive on the profficiency exam if the applicant studied the particular language for 8 years.
(Express answer to 3 significant digits)
(e) Interpret the value of the slope of the least-squares regression line in the context of this problem.
The model predicts that for each additional one year spent practicing, the grade on the proficiency exam
|
decreases |
||
|
increases |
by
points on average. (Express answer to 3 significant digits)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
