Question

If the coefficient of determination is equal to .80, what does that mean in regards to the two variables being tested?

If the p value is found to be equal to .0001, and we were using .05 significance, what does that indicate?

Discuss an original example of how regression and correlation analysis could be used by business, education, or the government.

Answer 1

If the coefficient of determination is equal to .80, it mean that for the two variables being tested, the 80% of variance in the dependent variable is being explained by the independent variable. Hence, Rsquare is 80%.

If p-value of .0001 is less than the significance value of .05, then it indicates that the independent variable in the regression, or the test is SIGNIFICANT. As a rule, if p-value< .05, then the variable is significant.

An example, businesses have used to analyze what does cement strength depend on, and then fined tuned cement making process and the composition to strengthen it further.

Lets say the we have a cement plant. The cement makers expleriments on how to increase the quality of cement. They do regression analysis and correlation analysis of various variables vs. the strength index of cement. Some examples of independent variables can be: Amount of SO2 as %age compposition, Amount of NO2 as %age of component, Time given for cement to cool down for hardening, No. of times cement was submerged in water to gain strength etc. If we find a set of variables which give a high Rsquare, then most probablty these variables are able to explain the strength of the cement. Correlation between each of the indepenent variables and the strength of cement is also helpful to know which variables effects strength of cement the most.