Categories
Mathematics

Statistics Data Regression/ Slope Analysis

1) For the first set of data a regression analysis (easiest to copy and paste into statcrunch).

  1. a) Find the correlation coefficient r.

.137

  1. b) Interpret correlation.

These variables have a weak, positive linear relationship.

  1. c) Find the slope

-.1428

  1. d) Find the intercept.

50.646

  1. e) Is regression worthwhile? Provide output and explanation justifying your answer.

Because there is not a robust linear relationship, the regression is not necessarily worthwhile.

  1. f) What is the predicted Y for X=40?

50.646+-.1428(40)

= 44.93

  1. g) Provide a scatter plot with regression line. (Statcrunch or Excel.)

  1. h) Provide a scatter plot with X vs the residuals.

  1. i) Do you see a pattern in h); if so describe?

No pattern

j)Complete the table on the next page. Include the result from sum of squares computation.

Advice: Do in Excel then copy and paste table into Word.

 

X1 Y1 x2 y2 x2-x1
86 4 7396 16 7380
43 4 1849 16 1833
74 46 5476 2116 3360
16 50 256 2500 -2244
38 69 1444 4761 -3317
30 61 900 3721 -2821
55 9 3025 81 2944
65 6 4225 36 4189
21 61 441 3721 -3280
0 71 0 5041 -5041
80 49 6400 2401 3999
13 3 169 9 160
28 34 784 1156 -372
98 91 9604 8281 1323
56 76 3136 5776 -2640
69 94 4761 8836 -4075
0 21 0 441 -441
0 77 0 5929 -5929
56 23 3136 529 2607
78 30 6084 900 5184
57 66 3249 4356 -1107
94 71 8836 5041 3795
92 12 8464 144 8320
90 14 8100 196 7904
14 69 196 4761 -4565
25 31 625 961 -336
34 4 1156 16 1140
64 86 4096 7396 -3300
18 59 324 3481 -3157
25 94 625 8836 -8211
80 11 6400 121 6279
63 40 3969 1600 2369
23 86 529 7396 -6867
73 58 5329 3364 1965
79 87 6241 7569 -1328
42 13 1764 169 1595
49 18 2401 324 2077
73 34 5329 1156 4173
20 71 400 5041 -4641
59 54 3481 2916 565
8 75 64 5625 -5561
43 40 1849 1600 249
93 38 8649 1444 7205
44 28 1936 784 1152
48 64 2304 4096 -1792
31 34 961 1156 -195
30 12 900 144 756
39 0 1521 0 1521
85 12 7225 144 7081
66 20 4356 400 3956

 

Sum of squares=200

2) Repeat a through i) (NOT j)) for the second set of data.

  1. a) Find the correlation coefficient r.

-.40

  1. b) Interpret correlation.

These two variables have a negative, linear relationship.

  1. c) Find the slope

-.531

  1. d) Find the intercept.

23.39

  1. e) Is regression worthwhile? Provide output and explanation justifying your answer.

Yes, the two variables have a significant (negative) linear relationship.

Because there is not a robust linear relationship, the regression is not necessarily worthwhile.

  1. f) What is the predicted Y for X=40?

23.388+–.531(40)

= 2.318

  1. g) Provide a scatter plot with regression line. (Statcrunch or Excel.)

  1. h) Provide a scatter plot with X vs the residuals.

  1. Do you see a pattern in h); if so describe?

No pattern

3) Repeat a through i) (NOT j)) for the third set of data.

1) For the first set of data a regression analysis (easiest to copy and paste into statcrunch).

  1. a) Find the correlation coefficient r.

.971

  1. b) Interpret correlation.

These variables have a strong, positive linear relationship.

c) Find the slope

8.34

  1. d) Find the intercept.

0

  1. e) Is regression worthwhile? Provide output and explanation justifying your answer.

Because there is a robust linear relationship, the regression is worthwhile.

  1. f) What is the predicted Y for X=40?

8.34(40)= 333.6

  1. g) Provide a scatter plot with regression line. (Statcrunch or Excel.)

  1. h) Provide a scatter plot with X vs the residuals.

  1. a) Find the correlation coefficient r.

.163

  1. b) Interpret correlation.

These variables have a strong non-linear relationship.

  1. c) Find the slope

.7533

  1. d) Find the intercept.

29.74

  1. e) Is regression worthwhile? Provide output and explanation justifying your answer.

No, this function is non-linear.

  1. f) What is the predicted Y for X=40?

29.732++.313(40)

= 42.52

  1. g) Provide a scatter plot with regression line. (Statcrunch or Excel.)

  1. h) Provide a scatter plot with X vs the residuals.

  1. i) Do you see a pattern in h); if so describe?

Nothing

6) What is the black swan effect? How does it relate to the concept of extrapolation?

Read ENTIRE Wikipedia article (feel free to do more research).

The black swan effect is a high impact low probability event.  It cannot be extrapolated.