Problem 3 :
Find 2 columns that are correlated.
Find 2 that aren't.
Estimate the temp when the wind is 25 mph, with uncertainty
Ozone Solar.R Wind Temp Day T - line
41 190 7.4 67 1 25.42394656
36 118 8 72 2 21.80113052

From the correlations

Temp vs Wind is correlated (p = 0.038 < 0.05)

Ozone vs Wind is NOT (p=0.09 > 0.05).

From the formula for the line,
T = - 0.7246 * (25 mph) + 73.97 = 56 mph

uncertainty in this due to T variation is about
about 2 * stdev(T-line) = 10

But slope, intercept are also uncertain.
So I'd up this a bit to something like

T = 56 +- 15 deg

or so. (That extra 5 deg is just a visual estimate
from the plot.)

12 149 12.6 74 3 20.35200411
18 313 11.5 62 4 29.04676259
23 313 14.3 56 5 33.39414183
28 305 14.9 66 6 26.14850976
23 299 8.6 65 7 26.87307297
19 99 13.8 59 8 31.22045221
8 19 20.1 61 9 29.7713258
8 194 8.6 69 10 23.97482014
7 225 6.9 74 11 20.35200411
16 256 9.7 69 12 23.97482014
11 290 9.2 66 13 26.14850976
14 274 10.9 68 14 24.69938335
18 65 13.2 58 15 31.94501542
14 334 11.5 64 16 27.59763618
34 307 12 66 17 26.14850976
6 78 18.4 57 18 32.66957862
30 322 11.5 68 19 24.69938335
11 44 9.7 62 20 29.04676259
1 8 9.7 59 21 31.22045221
11 320 16.6 73 22 21.07656732
4 25 9.7 61 23 29.7713258
32 92 12 61 24 29.7713258
28 66 16.6 57 25 32.66957862
28 266 14.9 58 26 31.94501542
28 100 8 57 27 32.66957862
23 13 12 67 28 25.42394656
45 252 14.9 81 29 15.28006166
115 223 5.7 79 30 16.72918808
37 279 7.4 76 31 18.9028777
n 31
r r_err p-value
wind vs temp -0.373276033 0.17227334 0.038608347 SIGNFICANT
temp vs ozone 0.439335272 0.166814425 0.013406207 SIGNIFICANT
temp vs solar 0.386536373 0.171262013 0.031715206 SIGNIFICANT
ozone vs wind -0.305524367 0.176816178 0.09463891 NOT SIGNIFICANT
= T at 25 mph
T = A * wind + B
A -0.724563207
B 73.9696814
wind 25
temp 55.85560123
4.966786831 T-line std dev