Question

Which of the following statements is NOT correct?

a. Ordinary least squares does not require any distributional assumptions
b. For a null hypothesis of the coefficient is 0, R has intuition about the alternative hypothesis
c. The null hypothesis is always this coefficient is equal to 0 for each test of slope or intercept
d. For the hypothesis test of the significance of each coefficient, we need a hypothesis, a test statistic, and the distribution of that test statistic when the null hypothesis is true

Answer 1

The incorrect statement is that Ordinary least squares does not require any distributional assumptions, as OLS assumes normality of errors for hypothesis testing.

Step-by-step explanation:

The statement which is NOT correct is: Ordinary least squares does not require any distributional assumptions.

Ordinary least squares (OLS) regression does indeed make several assumptions, including the normality of errors, especially when conducting hypothesis tests for significance. Referring to the hypothesis testing information provided, when testing the significance of a correlation coefficient, the null hypothesis states that there is no significant linear relationship between the variables (i.e., the population correlation coefficient is zero).

For the hypothesis testing of a regression coefficient, whether we are testing slope or intercept, the null hypothesis is commonly stated as the coefficient being equal to zero. But stating that R has an 'intuition' about the alternative hypothesis is not technically accurate; it is the researcher who specifies the alternative hypothesis, which might suggest a positive or negative association, depending on the research question. Moreover, it is indeed required to have a hypothesis, a test statistic, and to know the distribution of the test statistic when the null hypothesis is true, which could be based on the t-distribution or normal distribution for large sample sizes.