Question

1. Answer the following questions:

1. In the multiple explanatory variable regression model, define the partial correlation coefficients, explain how they are interpreted, and how do the interpretations differ from the coefficients of the single explanatory variable regression model?
2. Explain the t-tests of the partial correlation coefficients.  Have they changed?
3. Explain how the coefficient of determination has changed and why.
4. Explain how the null hypothesis has change for the F-test as compared to a single explanatory variable regression model.

Answer 1

A) Partial correlation coefficients measures the correlaaation between X and Y controlling for Z.

comparing th bivariate correlation to theett partial correlation. It allows to determine if the rrelattionship between X and Y direct or intervening.Interaction cannot be determined with partial correlation.

formula for Partial correlation:

rxyz = ryx- (ryz) (rxz) / 1- r2yz 1- r2xz

first calculate the zero order coefficient between all possible pairs of variables before solving the formula.

They are interpret by study all the effects of all the dependent variables simultaneously on a dependent variable. for ex the correlation coefficient bettween the yeild of paddy and the other variiables, viz. type of seedlings, manure, rainfall, humidity is the multiple correlation coefficient. this coefficient takes value between 0 to +1.

-difference between multiple and single correlation :

single correlation is the correlation between two variables. It is usually just called correlation.

multiple correlation is R2 which is measure of how much of the variation in a dependent variable is accounted for by a linear regreesion model.

B) a test used to test th significance of the correlation coefficient is the t- test. the purpose of the t-test for correlation is to test whether the population coeficient of correlation is significantly different from zero or close to zero.

C) coeffiecient of determination is a measure used in statistical analysis that assesses how well a model explains and predicts future outcomes. It is indicative of the level of explained variability in the data set.

It is reliled on heavily in trend analysis and is represented as a value between 0 and 1.

the closer the value is to 1, the better the fit, between the two factors. the value of 0 on the other hand would indicate that th model fails to accurately model the data at all. in economics an R2  vallue above 0.60 is seen as worthwhile.

D) In general if your calculated F- value in a test is larger than your f statistic you can reject the null hypothesis. you can the f statistic when deciding to support or reject the null hypothesis.