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 0 1 9 3 7 4 10 3 9 7 7 2 Books 13 12 7 10 12 13 10 12 9 6 8 12 Find the correlation coefficient: r=______ Round to 2 decimal places. The null and alternative hypotheses for correlation are: H0:H0: ? μ, ρ, or r = 0 H1:H1: ? ρ, r, or μ ≠0 The p-value is: ________ Round to 4 decimal places. 2. Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically significant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the regression line is useful. There is statistically insignificant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the use of the regression line is not appropriate. There is statistically significant evidence to conclude that a person who watches more movies will read fewer books than a person who watches fewer movies. There is statistically significant evidence to conclude that a person who watches fewer movies will read fewer books than a person who watches fewer movies. 3. r2=______ (Round to two decimal places) The equation of the linear regression line is: ˆy=_____ + _______x (Please show your answers to two decimal places) Use the model to predict the number of books read per year for someone who watches 4 movies per year. Books per year =________ (Please round your answer to the nearest whole number.)
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 | 0 | 1 | 9 | 3 | 7 | 4 | 10 | 3 | 9 | 7 | 7 | 2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Books | 13 | 12 | 7 | 10 | 12 | 13 | 10 | 12 | 9 | 6 | 8 | 12 |
- Find the
correlation coefficient : r=______ Round to 2 decimal places.
The null and alternative hypotheses for correlation are:
H0:H0: ? μ, ρ, or r = 0
H1:H1: ? ρ, r, or μ ≠0
The p-value is: ________ Round to 4 decimal places.
2. Use a level of significance of α=0.05α=0.05 to state the conclusion of the hypothesis test in the context of the study.
- There is statistically significant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the regression line is useful.
- There is statistically insignificant evidence to conclude that there is a correlation between the number of movies watched per year and the number of books read per year. Thus, the use of the regression line is not appropriate.
- There is statistically significant evidence to conclude that a person who watches more movies will read fewer books than a person who watches fewer movies.
- There is statistically significant evidence to conclude that a person who watches fewer movies will read fewer books than a person who watches fewer movies.
3. r2=______ (Round to two decimal places)
The equation of the linear regression line is:
ˆy=_____ + _______x (Please show your answers to two decimal places)
Use the model to predict the number of books read per year for someone who watches 4 movies per year.
Books per year =________ (Please round your answer to the nearest whole number.)
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