UW Statistics 311, Quiz 1 April 25, 2017

NOTE: 1. Write your name/student id on every page 2. No calculators / phones / computers 3. Use only the attached formula sheet and scratch paper 4. You get full credit for leaving numbers in simplified fractional form, but the questions have been designed to be easy to solve without calculators, and you may need to solve some of them to complete subsequent questions. GOOD LUCK! 1. Linear Regression (26 pts) The statistics below come from a study of spring temperature (in degrees centigrade) on almond crop output (in metric tons) at one orchard in California over time. The owner has asked you to describe the impact of temperature on output. Sample statistic x y s $ s% Cov(x, y) Value 12 10 2 10 10 Summarize the association by calculating the regression summaries for (Y|X), making sure to assign the roles of covariate and response as requested. Show your work using the table below: the calculation formula, the plug in values, and the final estimates. You may leave final estimates in fraction form, but simplifying the answers may be helpful for subsequent questions. (12 pts) NOTE: This is an “answer dependent” problem – if you get the earlier parts wrong, you will get the later parts wrong Statistic For example: z-score for x=6 Formula x, − x s $ Plugged in values 6 − 12 = 2 Final Estimates 6 − or − 3 2 1.1 r(x, y) Cov x, y s$ s% 10 2 ∗ 10 1 2 or 0.5 1.2 1.3 1.4 r 9 b= (Y|X) bA (Y|X) (r x, y )9 sy r x, y sx y − bx 1/2 9 or (0.5)9 1 10 10 ∗ or 0.5 ∗ 2 2 2 5 10 − 2.5 ∗ 12 or 5 − ∗ 12 2 1 4 or 0.25 5 2 or 2.5 -2