Warm-upCh.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 (E) An observational study

E#13 pg 769

Hypothesis Test for a Regression LineFirst, some equations you need to know.

You will never have to calculate it, but standard error of the slope

Test statistic:

xy 2

)ˆ( 2

n

yyseResidual standard

deviation

x

e

sn

sbSE

1)( 1

111

bSE

bt

Expected slope is 0 because the Ho always β = 0 The Ho is always that there is not relationship

Temperature and Marathon Runners Completing an Inference Test on slope Ho: β = 0 (This means that there is no relationship)

HA: β ≠ 0 (This means there is a relationship)

Seb is notgiven, but we can calculate it using t = b/Seb so Seb = t(b)

Confidence Interval with the same data

The P-value is pretty large. Implying that temperatures have no or little influence women’s race times.

C.I. for slope = b + tn-2* (seb)

H.W. E#16: Check conditions (sketch all three graphs) then answer a. to c. Pg 773 and 774 D#13 answer a. through d.

Problem A researcher from the state department of agriculture wants to know

ifthere is a relationship between the number of farms in operation andthe amount of acreage devoted to soybeans. He collects data from arandom sample of 21 countries in the state and records the number offarms (Farms) and the amount of acreage devoted to soybeanscultivation (Acreage in each of those countries. The scatter plot isshown in the following figure.

Is there a significant relationship between the amount of acreage devoted to soybean cultivationAnd the number of farms in this state? Give statisticalJustification to support your response (Use α = 0.01)

Step 1 and 2

Linearity

Equal Variance

Randomization

Normality

Step 3 and Step 4 State the regression equation, p-value, and draw a curve.

The computer output is: Predictor Coef Stdev t-ratio pConstant -0.636 1.458 -0.44 0.667# of Farms 0.29184 0.02641 11.05 0.000s = 4.120 R-sq = 85.9% R-sq(adj) = 85.2%

State the Conclusion

Homework 1) E#16 check conditions and solve a. to c. 2) D#13 pg 773 and 774 a. to d. 3)Read 8.3 and 8.4 ( We will cover these in 2 blocks).