From the regression output, find value of the correlation coefficient. Coefficients: Estimate Std. Error t value Pf(>|t|) (Intercept) 74.6816 3.3449 22.33 9.43e-12 *** X -3.5018 0.3219 -10.88 6.71e-08 *** Multiple R-Sq = 0.901 r=−0.949r=-0.949 r=0.901r=0.901 r=−3.5018r=-3.5018 r=−0.901r=-0.901 r=0.949r=0.949
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.
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From the regression output, find value of the
| Coefficients: | Estimate | Std. Error | t value | Pf(>|t|) |
| (Intercept) | 74.6816 | 3.3449 | 22.33 | 9.43e-12 *** |
| X | -3.5018 | 0.3219 | -10.88 | 6.71e-08 *** |
| Multiple R-Sq = 0.901 |
- r=−0.949r=-0.949
- r=0.901r=0.901
- r=−3.5018r=-3.5018
- r=−0.901r=-0.901
- r=0.949r=0.949
When we collect data for a study, why do we need to take extra care in the data collection process?
- To make sure we get the best data
- So we don't make any mistakes
- So that we can generalize
- To get the right average
- To avoid bias
From the data, find the least-squares regression line. What type of correlation is there?
| Study Hours | Test Score |
| 0 | 20 |
| 1 | 35 |
| 2 | 50 |
| 4 | 47.5 |
| 4 | 65 |
| 5 | 72.5 |
| 5 | 75 |
| 6 | 67.5 |
| 6 | 92.5 |
| 7 | 85 |
| 7 | 90 |
| 8 | 95 |
| 5 | 70 |
- y=9.051+24.765x.y=9.051+24.765x. There is
positive linear correlation. - y=24.765−9.051x.y=24.765-9.051x. There is negative linear correlation.
- y=24.765+9.051x.y=24.765+9.051x. There is positive linear correlation.
- y=−24.765+9.051x.y=-24.765+9.051x. There is negative linear correlation
- y=9.051−24.765x.y=9.051-24.765x. There is negative linear correlation.
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