Question

1. What is OLS regression? What are the limitations of OLS?

2. What are the null and research hypothesis for ANOVA? What is a limitation of the

ANOVA test?

3. Which test yields and f-statistic and what does this f-statistic represent?

Answer 1

1.) OLS means Ordinary Least Squares. A method of linear least squares used for finding out undisclosed parameters present in a model of linear regression. This method uses the principle of linear squares. It is the total of the squares if the difference between dependent variable and the predicted variable.

Limitations

• Poor characters of extrapolation
• Sensitivity to outliers
• Over long ranges, linear models can assume only limited shapes.
• Sensitive to unusual data points

2.) ANOVA helps to find out the mean difference of some independent groups. Null hypothesis of ANOVA shows that the mean will be same for all groups. Through the ANOVA test, an F-statistic will be generated and it can be used to calculate the p-value. If the value of p is less than 0.5, then the null hypothesis will be rejected.

A limitation to ANOVA test is that it considers only simple and independent random samples which are taken from a large lot. Therefore, the samples won't affect each other and measures should be taken repeatedly in order to get the accurate results.

3.) F-statistic is the ratio of the variances between groups to the variances within groups. When null hypothesis is true, taking ratio of two variables which are having an equivalent value and which yields the value of F-statistic near to 1.

ANOVA F test is used for yielding the F-statistic result.

While calculating F-statistic, if the F value is greater than computed F-statistic, then the hypothesis can be rejected. Along with F value, p value should also be considered. p value is the possibility that the results may have happened by chance and that can be find out with the help of F-statistic.