Question

TRUE or FALSE: Identify which of the following are valid statements and which ones are false. i. T F A ear odel is fit to a data set exhibiting a linear relationship. One of the data points is an outlier with respect to r, ie. its r-value is umisual compared to all other r-values but its y-value falls within the observed range of Y. Removing this data point likely change the estimated sample slope by a considerable amount ii. T F A correlation coefficient of r = 0.96 strongly suggests that changes in the explana- tory variable cause a change in the response variable. iii. T F The sampling variability of bi can be described by the sampling distribution of b Knowing the sampling distribution allows us to construct a confidence interval for the slope β1. iv. T F A hypothesis test for a significant linear relationship fails to reject null hypothesis Thus we can conclude that no near relationship exists between X and Y.

Answer 1

i.

The given statement is False.

Explanation -

A data point is an outlier when the y-value is unusual compared to all other y-values.

A data point is an influential point when the x-value is unusual compared to all other x-values and has a large effect on the slope of a regression line fitting the data.

ii.

The given statement is True.

Explanation -

A correlation coefficient of value near 1, suggests that explanatory and response variable is strongly correlated. Any change in one variable will cause a change in another variable.

iii.

The given statement is True.

Explanation -

Knowing the sampling distribution, we can calculate the mean and standard errors of b1 to construct a confidence interval of $\beta_1$ .

iv.

The given statement is False.

Explanation -

Failing to reject null hypothesis does not suggests that the null hypothesis is true. It only suggests that there is no significant evidence to reject the null hypothesis and conclude that a linear relationship exists between X and Y.