Question

Suppose we are interested in estimating the proportion of a population using a simple random sample of size n. i. State a suitable estimator of the population proportion as well as its sampling distribution. Mention any assumptions which you make. ii. Explain statistically how to determine the minimum sample size necessary to estimate a population proportion to within e units. iii. Provide a practical marketing example of a 95% confidence interval for a proportion. iv. Explain the purpose of the finite population correction factor (including a formula) and when it should be used.

Answer 1

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iv). We usually take a 95% level of significance to determine the confidence interval.

A 95% confidence level means that 95% of the intervals would include the parameter. This is a balanced levle of siginificance , not too low not too high.

1b) .Multicollinearity, its definition, disadvantages and detection.

Definition :- Multicollinearity is a phenomenon in which one predictor variable in a multiple regression model can be linearly predicted from the others with a substantial degree of accuracy.However, Multicollinearity does not reduce the predictive power .Instead it only affects calculations regarding individual predictors. That is, a multivariate regression model with collinear predictors can indicate how well the entire bundle of predictors predicts the outcome variable, but it may not give valid results about any individual predictor, or about which predictors are redundant with respect to others.

Issues :-

Multicollinearity causes the following two basic types of problems:

• The coefficient estimates can swing wildly based on which other independent variables are in the model. The coefficients become very sensitive to small changes in the model.
• Multicollinearity reduces the precision of the estimate coefficients, which weakens the statistical power of your regression model. You might not be able to trust the p-values to identify independent variables that are statistically significant.

Test /detection of multicollinearity:-

If We can identify which variables are affected by multicollinearity and the strength of the correlation,then we’re well on course to determining the multi collinearity . There is a very simple test to assess multicollinearity in our regression model. This is called as The variance inflation factor (VIF) which identifies correlation between independent variables and the strength of that correlation.

Few other methods of multi collinearity :-

Indicators that multicollinearity may be present in a model include the following:

1. Large changes in the estimated regression coefficients when a predictor variable is added or deleted
2. Insignificant regression coefficients for the affected variables in the multiple regression, but a rejection of the joint hypothesis that those coefficients are all zero (using an F-test)
3. If a multivariable regression finds an insignificant coefficient of a particular explanator, yet a simple linear regression of the explained variable on this explanatory variable shows its coefficient to be significantly different from zero, this situation indicates multicollinearity in the multivariable regression