Response to Student Tia Littleton
Your discussion correctly suggests that the R-squared value of 0.97 can be used for predictive purposes. In the analysis on the comparison of the amount, people spent to the amount they savings: It is correct to note that since the R-squared value ranges from 0 to 1, a value closer to 1 indicates that the variance of the independent variable highly explains the variance of the dependent variable. However, do you think you can use the R-squared value to tell whether the amount of money people spent to increase or decrease with those people spent? Similarly, on the analysis of the number of cops on the street and the number of reported crimes: You observe that the R-squared value of 0.40 cannot be used for predictive purposes. Don't you think that despite having a value closer to 0, it can be used to predict whether the two variables correlate in some way? Finally, your application of correlation analysis is relevant. You realize that correlation, unlike the regression factor R-squared value, can be used to establish whether two variables are positively or negatively related.
Response to Student Luke King
Your discussion correctly identifies the dependent and independent variables in the analysis of the comparison between the money people spent and save. Further, you correctly argue the meaning of the R-squared value of 0.97. As such, explain that 97% of the variance of the amount people save can be explained by the variance of the amount people spent. It is also true that despite the high value of the R-squared value, its usage for prediction depends on the circumstance. Whereas in some cases, the value being close to one assures predictability, in other cases, the 3% unexplained variance is a significant factor that makes it not used for prediction. However, on the analysis of the number of cops on the street and the cases reported, you think that the R-squared value is minimal to be used for any prediction. Don't you think it also depends on the circumstance of the analysis? Finally, your example of the usage of the R-squared value is relevant. Although, do you think you will be able to tell whether studying more increases with selection for promotion?
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