A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below. Movies 8 5 4 6 4 7 9 6 10 Books 0 2 7 0 7 0 0 0 0 r2r2 = (Round to two decimal places) Interpret r2r2 : There is a large variation in the number books people read each year, but if you only look at people who watch a fixed number of movies each year, this variation on average is reduced by 57%. Given any fixed number of movies watched per year, 57% of the population reads the predicted number of books per year.
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.
A study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below.
| Movies | 8 | 5 | 4 | 6 | 4 | 7 | 9 | 6 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| Books | 0 | 2 | 7 | 0 | 7 | 0 | 0 | 0 | 0 |
- r2r2 = (Round to two decimal places)
- Interpret r2r2 :
- There is a large variation in the number books people read each year, but if you only look at people who watch a fixed number of movies each year, this variation on average is reduced by 57%.
- Given any fixed number of movies watched per year, 57% of the population reads the predicted number of books per year.
- There is a 57% chance that the regression line will be a good predictor for the number of books people read based on the number of movies they watch each year.
- 57% of all people watch about the same number of movies as they read books each year.
- The equation of the linear regression line is:
ˆyy^ = + xx (Please show your answers to two decimal places) - Use the model to predict the number of books read per year for someone who watches 6 movies per year.
Books per year = (Please round your answer to the nearest whole number.) - Interpret the slope of the regression line in the context of the question:
- For every additional movie that people watch each year, there tends to be an average decrease of 1.07 books read.
- The slope has no practical meaning since people cannot read a negative number of books.
- As x goes up, y goes down.
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