Exam 12: Simple Linear Regression and Correlation

The sample correlation coefficient r equals -1 if and only if all $\left( x _ { i } , y _ { i } \right)$ pairs lie on a straight line with __________ slope.

A sample of n = 500 (x, y) pairs was collected and a test of $H _ { o } : \rho = 0 \text { versus } H _ { \pm } : \rho \neq 0$ was carried out. The resulting P-value was computed to be .00032. a. What conclusion would be appropriate at level of significance .001? b. Does this small P-value indicate that there is a very strong linear relationship between x and y (a value of $\rho$ that differs considerably from 0)? Explain.

If SSE = 36 and SST = 500, then the proportion of total variation that can be explained by the simple linear regression model is_ _________.

The estimated regression line or least squares line for the simple linear regression model is the line whose equation is given by __________.

In testing $H _ { 0 } : \beta _ { 1 } = 0$ versus $H _ { \pm } : \beta _ { 1 } \neq 0$ using a sample of 20 observations, the rejection region for .01 level of significance test is

Which of the following statements are true?