ASU Statistics Worksheet

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gebl27

Mathematics

Arizona State University

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Chapter 7 11. The following data represents the number of hits (x) and the number of strikeouts (y) for players on a college baseball team. Use the provided data below to complete parts a through f. 𝑋 π‘Œ 41 20 29 23 39 27 11 10 24 12 1 3 a. Use the above dataset to compute 𝛽̂ 0, 𝛽̂ 1, and the least squares line. (π‘₯ βˆ’ π‘₯Μ… ) (y-𝑦̅) (x-π‘₯Μ… )2 (y-𝑦̅)2 (x-π‘₯Μ… )(y-𝑦̅) βˆ‘ b. Calculate π‘Ÿ and 𝑅 2 . Interpret 𝑅 2 in the context of this baseball application. 𝑆𝑆𝐸 c. Complete the following ANOVA table. (Hint: R2 = 1 - 𝑇𝑆𝑆 or use slide 97) Source df Sum of Squares Mean Square F Regression Error Total d. Using the previous parts, complete a hypothesis test to assess how well number of hits predictors number of strikeouts. Use 𝛼 = 0.01 e. Construct and Interpret a 99% Confidence Interval for 𝛽1. f. How does your conclusions in parts b, d, and e confirm or contradict each other? g. Construct and Interpret a 90% Confidence Interval for Οƒ. h. Construct and Interpret a 95% Confidence Interval for the average y at a given x*. Where x* is 15. i. Using the same x* as in Part h, Construct and Interpret a 95% Prediction Limit for ynew at the given x*.
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Explanation & Answer:
9 Questions
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Explanation & Answer

View attached explanation and answer. Let me know if you have any questions.Here is the jmp output available. Finishing on the manual computations

JMP OUTPUT:
A-E

H-I

Confidence interval for part H and the prediction interval respectively as shown in row 7 for x= 15.In
Summary as shown Below

View attached explanation and answer. Let me know if you have any questions.

Chapter 7
11. The following data represents the number of hits (x) and the number of strikeouts (y) for players on a
college baseball team. Use the provided data below to complete parts a through f.
𝑋
π‘Œ

41
20

29
23

39
27

11
10

24
12

1
3

a. Use the above dataset to compute 𝛽̂ 0, 𝛽̂ 1, and the least squares line.
(π‘₯ βˆ’ π‘₯Μ… )

(y-𝑦̅)

(x-π‘₯Μ… )2

(y-𝑦̅)2

(x-π‘₯Μ… )(y-𝑦̅)

16.83333333
4.833333333
14.83333333
-13.16666667
-0.166666667
-23.16666667

4.166666667
7.166666667
11.16666667
-5.833333333
-3.833333333
-12.83333333

283.3611111
23.36111111
220.0277778
173.3611111
0.027777778
536.6944444
1236.833333

17.36111111
51.36111111
124.6944444
34.02777778
14.69444444
164.6944444
406.8333333

70.13888889
34.63888889
165.6388889
76.80555556
0.638888889
297.3055556
645.1666667

βˆ‘

𝛽̂ 1 = 645.167/1236.833 = 0.5216

Xbar =24.16666667 ybar =15.83333333
𝛽̂ 0 = 15.8333 – 0.5216*24.1667 = 3.2273
b. Calculate π‘Ÿ and 𝑅 2 . Interpret 𝑅 2 in the context of this baseball application.

(𝑦̂)

(y-𝑦̂)

(y-𝑦̂)2

24.61407
18.35453
23.57081
8.965234
15.7464
3.748956

-4.61407
4.645466
3.429187
1.034766
-3.7464
-0.74896

21.28963
21.58035
11.75933
1.070741
14.03548
0.560935
70.29646

Total=
R2 = 1- (70.296456/406.8333) = 0.8272
r= sqrt(R2) = sqrt(0.8272) = 0.9095

The r squared value indicates that 82.72% of the variation in number...


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