Hypothesis Testing and Type Errors

Module 5 - SLP HYPOTHESIS TESTING AND TYPE ERRORS
Name
Institution
Date
Regression analysis
Y=42.325+0.2632x
Coefficient of co-relation (multiple R) + 0.1132
Coefficient of determination (R squared) + 0.0128
xyDaysTime1422333584425246357408709551047115512481336144515421641
The regression analysis focuses on determining whether there is a pattern characterizing the data on time spent talking focusing on 16 observations. In any case, regression analysis helps to establish whether there is a relationship between the predictors, which are the independent variables and the dependent variables. This is based on the assumption that it is possible to predict observed data through fitting a model. As such, the predicted regression equation showed that the y intercept was 42.33 minutes. This was within the predicted range of 40-50 minutes. However, the regression analysis also highlights the coefficient of correlation and determination to indicate the strength of relationship between the variables.
Since the coefficient correlation is 0.1132 this shows that there is a weak relationship between dependent variable representing the days and time spent talking on the phone. One possible explanation of this is that the days cannot explain the variations in time spent talking on the phone. Values that lie between 0.1 and 0.5 have a weak positive relationship, but those below 0.1 show no relationship. On the other hand as the value of correlation coefficient nears 1, the relationship between the variables gets stronger. There is no distinction between the values of x and y in correlation analysis. In this case, the prediction ability of the regression analysis may not necessarily be sued to make predictions on the existence of a causal relationship. As such, looking at the unique factors that cause variations in time spent talking on the phone would provide more information. However, this is not a quantitative exercise, but the regression analysis is still useful to determine patterns.
The coefficient of determination also lies between 0 and 1, and a value of 0 indicates that no relationship exists between the variables, while 1 indicates a perfect linear relationship. For the 16 observations the coefficient of determination was 0.0128. The sum of squares of the regression is 23.55956, while the sum of squares of the residual is 1814.378, while the total sum of squares is 1837.938, whereby 0.0128 is equal 23.55956 divided by 1837.938....