Question
In: Math
The data below are the average monthly temperatures, in °F, and the monthly natural gas consumption,...
The data below are the average monthly temperatures, in °F, and the monthly natural gas consumption, in ccf, for a household in northwestern Pennsylvania.
a.)Test the significance of the correlation coefficient using α = 0.05 and the claim ρ < 0. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision
b.) Find the equation of the regression line for the given data
|
Temperature |
47 |
35 |
21 |
27 |
39 |
48 |
61 |
65 |
70 |
|||
|
Consumption |
34 |
169 |
248 |
134 |
137 |
100 |
19 |
34 |
12 |
Solutions
Expert Solution
| ( X) | ( Y) | X^2 | Y^2 | X*Y |
| 47 | 34 | 2209 | 1156 | 1598 |
| 35 | 169 | 1225 | 28561 | 5915 |
| 21 | 248 | 441 | 61504 | 5208 |
| 27 | 134 | 729 | 17956 | 3618 |
| 39 | 137 | 1521 | 18769 | 5343 |
| 48 | 100 | 2304 | 10000 | 4800 |
| 61 | 19 | 3721 | 361 | 1159 |
| 65 | 34 | 4225 | 1156 | 2210 |
| 70 | 12 | 4900 | 144 | 840 |
| Line of Regression Y on X i.e Y = bo + b1 X | ||||
| X | Y | (Xi - Mean)^2 | (Yi - Mean)^2 | (Xi-Mean)*(Yi-Mean) |
| 47 | 34 | 1.235 | 4167.425 | -71.728 |
| 35 | 169 | 118.568 | 4962.413 | -767.062 |
| 21 | 248 | 619.457 | 22333.629 | -3719.507 |
| 27 | 134 | 356.791 | 1256.305 | -669.506 |
| 39 | 137 | 47.457 | 1477.972 | -264.84 |
| 48 | 100 | 4.457 | 2.086 | 3.049 |
| 61 | 19 | 228.345 | 6329.093 | -1202.173 |
| 65 | 34 | 365.234 | 4167.425 | -1233.729 |
| 70 | 12 | 581.345 | 7491.872 | -2086.951 |
milcah answered 11 months agoRelated Solutions
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10 18 ??? 25 26 20 11
If the median average monthly temperature for this period is 20
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d.
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9,3571,1976,0.525,541
9,4092,1250,0.572,524
9,3865,1586,0.58,561
7.5,4870,2351,0.529,414
8,4399,431,0.544,410
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8,4447,8577,0.529,464
7,4512,8507,0.552,498
8,4391,5939,0.53,580
7.5,5126,14186,0.525,471
7,4817,6930,0.574,525
7,4207,6580,0.545,508
7,4332,8159,0.608,566
7,4318,10340,0.586,635
7,4206,8508,0.572,603
7,3718,4725,0.54,714
7,4716,5915,0.724,865
8.5,4341,6010,0.677,640
7,4593,7834,0.663,649
8,4983,602,0.602,540
9,4897,2449,0.511,464
9,4258,4686,0.517,547
8.5,4574,2619,0.551,460
9,3721,4746,0.544,566
8,3448,5399,0.548,577
7.5,3846,9061,0.579,631
8,4188,5975,0.563,574
9,3601,4650,0.493,534
7,3640,6905,0.518,571
7,3333,6594,0.513,554
8,3063,6524,0.578,577
7.5,3357,4121,0.547,628
8,3528,3495,0.487,487
6.58,3802,7834,0.629,644
5,4045,17782,0.566,640
7,3897,6385,0.586,704
8.5,3635,3274,0.663,648
7,4345,3905,0.672,968
7,4449,4639,0.626,587
7,3656,3985,0.563,699
7,4300,3635,0.603,632
7,3745,2611,0.508,591
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3
10
14
22
28
31
33
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57
37
24
-5
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Below is the scatterplot of this data with the best-fit
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The sample data below shows the average temperature (x,
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Enter your answer as a decimal rounded to three
places.
Correlation coefficient =
Average temperature
Monthly
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29
326
36
295
42
241
58
196
62
154
70
93
74
33
77
0
68
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57
184
45
263
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