Simple linear regression results: Dependent Variable: Grade (Marks) Independent Variable: Absences Grade (Marks) = 89.100971 - 3.1906331 Absences Sample size: 30 R (correlation coefficient) = -0.93164951 R-sq = 0.86797081 Estimate of error standard deviation: 3.2600128 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 89.100971 1.1464745 ≠ 0 28 77.717357 <0.0001 Slope -3.1906331 0.23516911 ≠ 0 28 -13.567399 <0.0001 Analysis of variance table for regression model: Source DF SS MS F-stat P-value Model 1 1956.2835 1956.2835 184.07431 <0.0001 Error 28 297.57514 10.627684 Total 29 2253.8587 a) Interpret the slope in terms of abscences and grade. b) Does y-intercept have meaning? If so, what is it?
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.
Simple linear regression results:
Dependent Variable: Grade (Marks)
Independent Variable: Absences
Grade (Marks) = 89.100971 - 3.1906331 Absences
Sample size: 30
R (
R-sq = 0.86797081
Estimate of error standard deviation: 3.2600128
Parameter estimates:
| Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
|---|---|---|---|---|---|---|
| Intercept | 89.100971 | 1.1464745 | ≠ 0 | 28 | 77.717357 | <0.0001 |
| Slope | -3.1906331 | 0.23516911 | ≠ 0 | 28 | -13.567399 | <0.0001 |
Analysis of variance table for regression model:
| Source | DF | SS | MS | F-stat | P-value |
|---|---|---|---|---|---|
| Model | 1 | 1956.2835 | 1956.2835 | 184.07431 | <0.0001 |
| Error | 28 | 297.57514 | 10.627684 | ||
| Total | 29 | 2253.8587 |
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