Math 201 Basic Statistics Regression Analysis

Math 201 Module 5 SLP
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Course: Math 201 Basic Statistics
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Regression analysis
Data set
DayTime135238349432540637738834945103111401238133614351533Regression equation: y= 39.6286 - 0.2786 x
Coefficient of correlation = -0.2599
Coefficient of determination =0.0676
Explanation
The regression analysis focuses on the statistical relationship between the predictor variable (s) and the outcome (Wang & Jain, 2003). In this case, the outcome was the time spent driving in the weekdays from home to work while the team series representing the days was assumed to be the predictor variable. Consequently, the y intercept was 39.63 minutes, and although it appears meaningless, the average time spent on the road to and from work was more likely to be close to 40 minutes. Nonetheless, the main reason for including the constant is that the mean of the residuals is then zero, and living the constant would result in a biased prediction. The implication of the regression analysis is that for each subsequent day the time spent driving to and from work is likely to decrease by 0.28 minutes. The coefficient of the independent variables (days), indicates the size of the effect on driving time (dependent) variable, and size it is a negative sign it indicates the direction of the effect. The assumption of linear regression makes it easier to evaluate the relationship of the coefficients to the outcome compared to logistic and probit regression (Wang & Jain, 2003).
The Coefficient of correlation was -0.2599 and this assesses how the least squares fit the observed data. In this case, the association of the days in progression to the driving time was a negative correlation showing a weak relationship between the two variables. Even though, the weak relationship shows that the number of days cannot wholly explain the variations in the driving time to and from work, it cannot be ruled out that the time would likely be less as days progressed. The rationale for this is that the coefficient of correlation has a negative sign. In any case, the coefficient is not below 0.1, which shows that the relationship is virtually nonexistent. It is necessary to identify factors that caused variations in driving time, since the coefficient merely helps to identify the strength of the causal relationship. Determining the emerging patterns is possible by taking into account the coefficient and regression analysis.
The coefficient of determination was 0.0676 and is the coefficient of correlation squared indicated that there was also a weak relationship between the predictor and outcome. The higher the coefficients the stronger the relationship between the variables, but the coefficient of correlation can have a negative sign or positive sign but the correlation of determination has a positive sign (Cios, 2007). ...