For Question 14, from part (a)-(f) lultion 14.5 31.9 32.0 165 Averages 1488 12.1

Question

For Question 14, from part (a)-(f)

lultion 14.5 31.9 32.0 165 Averages 1488 12.12 3106 27.78 14.88 12.12 31.06 27.78 Residuals 11.0 26.2 23.8 12.7 10.8 140 143 35.7* 25.0 128 10.0 40.1* 29.3 62 2.38 0.844.22 21.3 28.8 = 14.88 3.52 -1.12 -486 3.98 12.12 31.06 2778-2.18 132 -76 1.02 14.88 12.12 31.06 27.78 0.88 2.18 464 17 14.88 12.12 31.06 27.782.08 -2.12 9.04 1.52 Foke data: The effect of adding constants or maltiplhing by constamts. Decompose each of 13 the following fake data count degrees of freedom. Write your SSs and dfs under the boxes of your decomposition Then compute SD = VMSRes For these fake data sets, all the arithmetic should involve only whole numbers. Parts (a)-(e) are related to each other and to the next two questions: look for patterns as you do the arithmetic. sets into average plus residuals. Then compute sums of squares a nd b. d. e. | 120 80 C. 201 -201 L | 102 | 98 a. 12 8 4. Mark the following statements true or fale. In trying to decide, you might refer to your nu merical results from Exercise 13, and you might rely also on any intuitive ideas you have about what ought to be true of a number that measures how spread out the data are. If you add 100 to every number in a data set, the SD goes up by 100. a.

Explanation / Answer

15.

a. The new SD will become c square times the if you multipy each number with c

So, new SD will equal the old SD times c^2

b. If SD =5, multiple every no. by 3, then add 10 to every number, the SD will equal = 5*3^2 = 45

Var(aX+b) = a^2 Var(X) + Var(b) = a^2*Var(X)+0 = a^2Var(X)

c.

If SD = 5, then 10 is added to each number, and then multiply every no. by 3, then new SD will be equal to 9 times old SD = 9*5 = 45

Var(a(X+b)) = a^2 Var(X) + Var(ab) = a^2*Var(X)+0 = a^2Var(X)

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