Question 1a and 1b x 4.pdfework 4.pdf (92 KB)S1. Consider the following dataXy243247505968746250413021185.79 214.47 288.03 424.84 454.68 539.03 621.55 675.06 562.03 452.93 369.95 273.98and assume that steam usage and average temperature are jointly normally distributed.(a) Find the correlation between steam usage and monthly average ambient temperature.(b) Test the hypothesis that p 0 using a 0.05.You can use R for the calculation of the summary statistics, but you should show your work.2. Suppose you observe a correlation r = 0.5 between two variables in a sample of n 14 subjects.Can you conclude that the two variables are correlated in the population? (Hint: perform ahypothesis test using a = 0.05).3. How large muust a correlation r be in order to be significantly different from zero (at the 0.05

1a) From the given information, x y x^2 y^2 xy 21 185.79 441 34517.92 3901.59 24 214.47 576…

Answered: Consider the following data X y 21 24…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question 1a and 1b

x 4.pdf
ework 4.pdf (92 KB)
S
1. Consider the following data
X
y
24
32
47
50
59
68
74
62
50
41
30
21
185.79 214.47 288.03 424.84 454.68 539.03 621.55 675.06 562.03 452.93 369.95 273.98
and assume that steam usage and average temperature are jointly normally distributed.
(a) Find the correlation between steam usage and monthly average ambient temperature.
(b) Test the hypothesis that p 0 using a 0.05.
You can use R for the calculation of the summary statistics, but you should show your work.
2. Suppose you observe a correlation r = 0.5 between two variables in a sample of n 14 subjects.
Can you conclude that the two variables are correlated in the population? (Hint: perform a
hypothesis test using a = 0.05).
3. How large muust a correlation r be in order to be significantly different from zero (at the 0.05

Expert Solution

Step 1

1a)

From the given information,

x	y	x^2	y^2	xy
21	185.79	441	34517.92	3901.59
24	214.47	576	45997.38	5147.28
32	288.03	1024	82961.28	9216.96
47	424.84	2209	180489	19967.48
50	454.68	2500	206733.9	22734
59	539.03	3481	290553.3	31802.77
68	621.55	4624	386324.4	42265.4
74	675.06	5476	455706	49954.44
62	562.03	3844	315877.7	34845.86
50	452.93	2500	205145.6	22646.5
41	369.95	1681	136863	15167.95
30	273.98	900	75065.04	8219.4
∑X=558	∑y=5062.34	∑x^2=29256	∑y^2=2416235	∑xy=265869.6

Correlation:

$r = \frac{n \sum x y - \sum x \sum y}{\sqrt{[n \sum x^{2} - {(\sum x)}^{2}] [n \sum y^{2} - {(\sum y)}^{2}]}} = \frac{(12 * 265869.6) - (558 * 5062.34)}{\sqrt{[(12 * 29256) - 558^{2}] [(12 * 2416235) - 5062 . 34^{2}]}} = \frac{365649.8}{365674.5} = 0.9999$