Week 5 Assignment


The last month has been a fairly hectic one for me as I've transitioned from working 3 jobs for a short time, down to 2 and am just beginning to create the semblance of a regular schedule again. Something I've been wondering about in the midst of the transition, is how the variation in my sleep patterns effects me on a day to day basis.

This project is a great way to explore that; my project will take a look at the number of minutes I sleep compared to the amount I spend per day on discretionary purchases. For the purposes of this project, I'll be excluding regular living expenses (i.e., rent, utilities, gas, weekly groceries, etc) so as not to skew the data with purchases that occur on a regular basis regardless of sleep.

My hypothesis is that there will be a moderately strong negative correlation between minutes of sleep and dollars spent each day; my reasoning being that I'm significantly less likely to have woken with enough time to prepare for the day after a night with relatively little sleep, meaning I'll be more likely to spend money on coffee, lunch and the like.

Week 14 Assignment

Project.jpg

r = 0.0409
Least Squares Regression Equation: y = 0.0068x+12.2755

r^2 = 0.0017

It is clear, based on the data collected and the subsequent analysis that there is no linear relationship between the amount of time that I sleep, and the amount of money I spend in a day. What incidental correlation does appear to exist is positive rather than negative, which is directly opposed to my hypothesis. There are numerous variables which could play into this, though the primary explanatory factor I see is that regardless of how much or little sleep one gets one tends to rationalize purchases before making them, so that subjective need rather than mental state (assuming one is still functioning on some level) determines the amount one spends. Additionally, I suspect that there is a compensatory factor at play, whereby I may have abstained from making a purchase I otherwise would have, because I'd already spent money in a transaction I might not have made had I gotten more sleep (i.e., bought lunch, to refer to the example given in my original hypothesis).

When I removed the outliers (in a subjective, not a statistical sense--meaning in this case, days where I spent no money, and days where I spent more than $60.00, each case of which was exceptional) in an attempt to create a data set more representative of standard spending, a much stronger correlation appeared, though it remained positive rather than my predicted negative. The new values (which I will not analyze here as it was not a part of my original proposal, though it would be interesting to look at in more depth) were:
r =.3308
Least Squares Regression Equation: y = 0.0278x+4.2933
r^2 = .1094

While our r value in this instance is still well below the critical value provided in Appendix A table II of our text, it is far closer to than the original r value.

My original data set is as follows:

Date
Time Slept (M)
Money Spent
25-Feb
255
21.81
26-Feb
270
27.63
27-Feb
375
12.15
28-Feb
490
0
Mar-13
375
11.23
2-Mar
512
38.62
3-Mar
280
23.12
4-Mar
330
12.34
5-Mar
450
0
6-Mar
225
0
7-Mar
270
6.43
8-Mar
120
9.21
9-Mar
480
22.07
10-Mar
265
0
11-Mar
420
5.34
12-Mar
350
21.69
13-Mar
425
22.87
14-Mar
360
0
15-Mar
420
63.52
16-Mar
240
8.23
17-Mar
260
82.49
18-Mar
260
7.13
19-Mar
330
6.87
20-Mar
460
1.27
21-Mar
385
15.12
22-Mar
420
14
23-Mar
315
9.13
24-Mar
510
0
25-Mar
350
10.82
26-Mar
290
8
27-Mar
400
0.87