27 - It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students. NOTE: Only partial output is shown. The value of the measured t-test statistic to test whether mean SALARY depends linearly on HOURS is Regression Statistics Multiple R R Square Adjusted R Square 0.8857 0.7845 0.7801 Standard Error 1.3704 Observations 51 ANOVA df SS MS F Significance F Regression Residual 1 335.0472 335.0473 178.3859 1.8782 Total 50 427.0798 Standard Coefficients Error t Stat P-value Lower 95% Upper 95% Intercept Hours -1.8940 0.4018 -4.7134 0.0000 -2.7015 -1.0865 0.9795 0.0733 13.3561 0.0000 0.8321 1.1269 Note: 2.051E-05 = 2.051*10 and 5.944E – 18 =5.944*10-18
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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