1. Warm-up Ch.11 Inference for Linear Regression Day 2 1. Which of the following are true statements? I. By the Law of Large Numbers, the mean of a random variable will get closer and closer to a specific value II. The standard deviation of a random variable is never negative. III. The standard deviation of a random variable is 0 only if the random variable takes a lone single value. (A) I and II (B) I and III (C) II and III (D) I, II, and III (E) None of the above 2. Which of the following is most useful in establishing cause-and- effect relationships? (A) A complete census (B) A least squares regression line showing high correlation (C) A simple random sample (SRS) (D) A controlled experiment

2. Hypothesis Test for a Regression Line First, some equations you need to know. You will never have to calculate it, but standard error of the slope Test statistic: Residual standard deviation Expected slope is 0 because the H o is almost always β = 0.

3. Temperature and Marathon Runners Completing an Inference Test on slope H o : β = 0 (This means that there is no relationship) H A : β ≠ 0 (This means there is a relationship) Se b is not given, but we can calculate it using t = b/Se b so Se b = t(b)

5. Problem A researcher from the state department of agriculture wants to know if there is a relationship between the number of farms in operation and the amount of acreage devoted to soybeans. He collects data from a random sample of 21 countries in the state and records the number of farms (Farms) and the amount of acreage devoted to soybeans cultivation (Acreage in each of those countries. The scatter plot is shown in the following figure. Is there a significant relationship between the amount of acreage devoted to soybean cultivation And the number of farms in this state? Give statistical Justification to support your response (Use α = 0.01)

6. Step 1 and 2 Linearity Equal Variance Randomization Normality

7. Step 3 and Step 4 State the regression equation, p-value, and draw a curve. The computer output is: PredictorCoefStdevt-ratiop Constant-0.6361.458-0.440.667 # of Farms0.291840.0264111.050.000 s = 4.120R-sq = 85.9% R-sq(adj) = 85.2% State the Conclusion H.W. 11.2 P#11 and P#13 a – c for b sketch the residual plot and complete a histogram of the residuals (not dotplot)