a. Dependent variable: starting salary The regression equation is Ŷ = X + , where Ŷ is the predicted value of and X is the value of . The Pearson correlation between college GPA and starting salary is . You believe there is a linear relationship between college GPA and starting salary. You conduct a hypothesis test with the null hypothesis H00 : β11 = 0 versus the alternative hypothesis H11: β11 ≠ 0. Based on these results, with a significance level of α = .05, you reject the null hypothesis. You conclude that college GPA and starting salary are linearly related.
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.
|
|
Mean
|
Std Deviation
|
N
|
|---|---|---|---|
| Starting salary | 51.159 | 10.945 | 50 |
| College GPA | 3.064 | 0.5574 | 50 |
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std Error of the Estimate
|
|---|---|---|---|---|
| 1 | 0.206ª | 0.0426 | 0.0227 | 10.8205 |
|
Model
|
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Two-Tailed Sig
|
|---|---|---|---|---|---|---|
| 1 | Regression | 250.15 | 1 | 250.15 | 2.1365 | 0.1503bb |
| Residual | 5,619.98 | 48 | 117.08 | |||
| Total | 5,870.13 | 49 |
|
|
Unstandardized Coefficients
|
Standardized Coefficients
|
Beta
|
t
|
Two-Tailed Sig
|
|
|---|---|---|---|---|---|---|
|
Model
|
B
|
Std Error
|
||||
| 1 | (Constant) | 38.739 | 8.6335 | 4.4871 | 0.0001 | |
| College GPA | 4.0534 | 2.7731 | 0.206 | 1.4617 | 0.1503 |
a)
The regression line is
y = 38.739 + 4.0534X
where Ŷ is the predicted value of starting salary and X is the value of College GPA
b)
Pearson correlation between college GPA and starting salary is 0.206
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