You are given the following data, where X1X1 (years of working experience at current position) and X2X2 (salary in thousands) are used to predict YY (morale): YY X1X1 X2X2 115 4 45 120 2 33 180 7 38 170 7 49 115 2 28 185 3 31 125 1 24 170 6 40 180 10 52 Determine the following multiple regression values. Report intercept and slopes for regression equation accurate to 3 decimal places: Intercept: a= Partial slope X1X1: b1= Partial slope X2X2: b2= Report sum of squares and coefficient of multiple determination accurate to 3 decimal places: R2= SSTotal= Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places): F-ratio = P-value = Report the variance of the residuals accurate to 3 decimal places: MSres= Report the results for the hypothesis test for the significance of the partial slope for salary (report the test statistic for the regression coefficients accurate to 3 decimal places and P-value accurate to 4 decimal places): t2= P-value =
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.
You are given the following data, where X1X1 (years of working experience at current position) and X2X2 (salary in thousands) are used to predict YY (morale):
| YY | X1X1 | X2X2 |
|---|---|---|
| 115 | 4 | 45 |
| 120 | 2 | 33 |
| 180 | 7 | 38 |
| 170 | 7 | 49 |
| 115 | 2 | 28 |
| 185 | 3 | 31 |
| 125 | 1 | 24 |
| 170 | 6 | 40 |
| 180 | 10 | 52 |
Determine the following multiple regression values.
Report intercept and slopes for regression equation accurate to 3 decimal places:
Intercept: a=
Partial slope X1X1: b1=
Partial slope X2X2: b2=
Report sum of squares and coefficient of multiple determination accurate to 3 decimal places:
R2=
SSTotal=
Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places):
F-ratio =
P-value =
Report the variance of the residuals accurate to 3 decimal places:
MSres=
Report the results for the hypothesis test for the significance of the partial slope for salary (report the test statistic for the regression coefficients accurate to 3 decimal places and P-value accurate to 4 decimal places):
t2=
P-value =
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