The strength of a linear relationship

The strength of a linear relationship

• The strength of a linear relationship is determined by the correlation coefficient and visually by a scatter plot. The scatter plot above represents a weak positive relationship between GPA and act. The points do not lie on a straight line; they are scattered on the right side, indicating a weak linear relationship.

• The correlation coefficient for GPA and act is 0.2694, with a confidence interval of 0.0781 to 0.4766. Representing a weak positive correlation between GPA and act. The confidence interval does not include zero, and the correlation between GPA and act statistically exists.

• The fitted logistic regression is statistically significant, with an F statistic score of 9.24 and a p-value of 0.002917. the adjusted R square for the model is 0.06476. implying that the model with one explanatory variable can account for about 6% of the variance occurring on the GPA due to the prediction. Additionally, the intercept’s confidence interval does not contain zero, and thus the model is statistically significant. We can, therefore, conclude that there exists a linear relationship between GPA and act.

• Generally, the coefficients from the model are equivalent to b0=2.114 and b1=0.382. There is a slight difference in confidence intervals for the coefficients, whereby the confidence interval for the nonparametric bootstrap is more comprehensive than the confidence interval for the logistic regression. Most importantly, both the confidence intervals contain the estimated coefficients.

• The models have been fitted using the AIC information criteria. The error rate is the determinant of the best model among the fitted models. Accessing the models’ error rates, the logistic regression model produces the lowest error rate of 256. We recommended logistic regression in the min_project_31 since it had the least error rate and highest sensitivity score. Likewise, in this mini_project_41, we recommend logistic regression too.