A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y). The results of the regression were: y=ax+b a=-0.889 b=31.442 r2=0.3721 r=-0.61 Use this to predict the number of situps a person who watches 4 hours of TV can do (to one decimal place)
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.
![**Analysis of the Relationship Between TV Watching and Number of Sit-ups**
A regression analysis was performed to examine whether there is a relationship between the number of hours of TV watched per day (x) and the number of sit-ups a person can perform (y).
**Regression Results:**
- Regression Equation: \( y = ax + b \)
- Slope (\( a \)): \( -0.889 \)
- Intercept (\( b \)): \( 31.442 \)
- Coefficient of Determination (\( r^2 \)): \( 0.3721 \)
- Correlation Coefficient (\( r \)): \( -0.61 \)
**Explanation:**
- The negative slope (\( a = -0.889 \)) indicates that as the number of hours of TV watched per day increases, the number of sit-ups a person can perform decreases.
- The intercept (\( b = 31.442 \)) represents the predicted number of sit-ups a person can do if they watch 0 hours of TV per day.
- The coefficient of determination (\( r^2 = 0.3721 \)) signifies that approximately 37.21% of the variation in the number of sit-ups can be explained by the number of hours of TV watched.
- The negative correlation coefficient (\( r = -0.61 \)) indicates a moderate negative relationship between TV watching hours and the number of sit-ups.
**Prediction:**
To predict the number of sit-ups a person who watches 4 hours of TV per day can do, apply the regression equation:
\[ y = ax + b \]
\[ y = (-0.889 \times 4) + 31.442 \]
\[ y = -3.556 + 31.442 \]
\[ y = 27.9 \]
Therefore, a person who watches 4 hours of TV per day is predicted to be able to do 27.9 sit-ups.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcebbde0b-56df-456f-b45f-057baf1d3a0f%2Fef520dc1-3df3-4ef5-9283-eabfbc80877c%2F9mka9m_processed.png&w=3840&q=75)
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