Inference for Regression. A random sample of 79 patients from a walk-in clinic records the low- and high-density cholesterol levels of the patients, labeled LDL and HDL, respectively. LDL is often referred to as "bad" choles- terol, while HDL is often referred to as "good" cholesterol. A researcher de- cides to use least-squares regression to estimate the population regression line relating LDL (y) and HDL (x) levels: My = a + Bx The results from the analysis include: est. of s a = 25 6 = 0.75 SE. = 3 SEb = 0.025 $ = 50 (regression standard error) 72 = 0.810 n = 79 (a) We want to test whether or not there is a statistically significant linear re- lationship between a and y. State the corresponding null and alternative hypotheses in scientific notation. (b) What is the value of the test statistic for the test? (c) What is the sampling distribution for this test statistic? (d) What is the P-value of the test? (e) What is a 90% confidence interval for the slope in the simple linear re- gression model? (f) Based on the confidence interval constructed in part (e), can we reject Ho in favour of Hi at the a = 0.1 level? You must justify your answer. (g) What are the two most important figures (to construct and examine) to "check" the conditions for linear regression inference