On Homework Assignment 1, the general consensus was that I was not in a relationship. Although I definitly did not ask for your opinions... many of you commented that I have some psychological work to do before entering into a committed relationship. Since then, I have collected psychological data from a group of people, measuring their “Big Five” traits: Openness, Conscientiousness, Extroversion, Agreeableness, and Neuroticism. I also had these people provide a “Relationship Satisfaction Score” on a continuous scale from 0 to 100. (You can assume that the experiment was conducted well, the sampling was done properly, etc.) For our purposes, we’ll say that anybody with a Relationship Satisfaction Score of 70 or greater is in a “good relationship”, and anybody with a Relationship Satisfaction Score below 70 is in a “bad relationship”. Assume that I have the following profile: Trait                                        Score Openness                               70 Conscientiousness                 100 Extroversion                            80 Agreeableness                        60 Neuroticism                             90 Using the information provided here, the data in the “Relationships” sheet, and the “Problem 1 Regression Output” image: a) Are any of the variables irrelevant, statistically speaking? b) Assuming that I want to be in a relationship, which of the following variables would I want to work on increasing, and which should I try to minimize? How can we tell? c) How much variability is being explained by this model, and which metric is telling you that? d) The residual plots from the regression analysis are provided. Using these plots, verify that all of the regression assumptions are met. e) Comment on the overall adequacy of the linear model that we built. f) What is my projected Relationship Satisfaction Score, and do I have a shot at a good relationship?       Data Set  Neuroticism Openness Conscientiousness Agreeableness Extroversion RELATIONSHIP SATISFACTION SCORE 163.5  70.1  52.3  93.1  78.2  51 9.9  99  179  91.1  84.5  75 6.7  97.9  91.9  86.5  88.4  76 22.2  84.3  39.8  94.6  92.4  72 128.6  56  8.1  81.3  60.6  48 17.6  93.4  95.6  91.7  91.3  78 4.7  98.8  187.6  94.8  97  77 27.1  89.5  94.2  95.5  90.4  73 15.9  84.5  66.4  95.2  95.5  72 100.3  93.9  256.2  56.5  56  54 51.8  67.8  5.8  37.2  32.5  61 3.6  99.8  208.5  97.7  97  76 72.9  50  17.5  68.2  70.4  58 4.8  97.2  251  98.8  99.3  81 32  75.2  47.6  98.6  97.5  69 101.2  41  10.2  85.2  72.1  55 129.1  54.2  12.4  76.7  73.3  50 22.9  84.8  38.2  94.8  97  74 6.2  99  203.1  97.8  98.3  75 3.8  98.9  324  99.6  98.5  82 19.1  92.6  59.3  90.8  90.7  74 8.7  99.8  177  95  96.8  74 99.6  89.6  20.5  72.2  75.3  50 5.4  99.7  196.4  95.6  95.8  74 128  31.1  10.4  70.6  60.8  51 84  58  24  72.8  76  59 16.2  93.1  153.9  99.2  99.9  75 27.5  97.4  42.9  99.6  98.5  68 89.7  56.1  9.7  94.6  89.4  53 38.7  88.8  65.6  83.8  88.5  65 123.7  61.3  22.9  60.1  54.8  53 18.5  94.1  145.1  99.1  98.2  77 22  93.9  53.9  84.4  83.9  75 5  99.5  204.3  96.9  96.7  76 3.6  95.2  244.4  99.1  99.7  80 7.4  96.3  864.4  95.7  96.6  82 17.6  98.5  36.4  90.1  90.1  71 12.2  97.7  151.2  87.9  87.3  74 8.6  86.6  247  96.7  96.5  76

Need help with parts (a) to (f) on this Intro to Probability and Statistics homework problem. You can use Excel to help you complete this problem. Below the the homework problem, is the data set in Excel that goes with this problem and the problem 1 Regression output image. Make sure the answers that you provide are lengthy. Also, make sure your handwriting is neat and readable.

Homework Problem

On Homework Assignment 1, the general consensus was that I was not in a relationship.
Although I definitly did not ask for your opinions... many of you commented
that I have some psychological work to do before entering into a committed
relationship.

Since then, I have collected psychological data from a group of people, measuring
their “Big Five” traits: Openness, Conscientiousness, Extroversion, Agreeableness,
and Neuroticism. I also had these people provide a “Relationship Satisfaction
Score” on a continuous scale from 0 to 100. (You can assume that the experiment
was conducted well, the sampling was done properly, etc.)

For our purposes, we’ll say that anybody with a Relationship Satisfaction Score
of 70 or greater is in a “good relationship”, and anybody with a Relationship
Satisfaction Score below 70 is in a “bad relationship”. Assume that I have the
following profile:

Trait                                        Score
Openness                               70
Conscientiousness                 100
Extroversion                            80
Agreeableness                        60
Neuroticism                             90

Using the information provided here, the data in the “Relationships” sheet, and
the “Problem 1 Regression Output” image:

a) Are any of the variables irrelevant, statistically speaking?

b) Assuming that I want to be in a relationship, which of the following
variables would I want to work on increasing, and which should I try
to minimize? How can we tell?

c) How much variability is being explained by this model, and which metric
is telling you that?

d) The residual plots from the regression analysis are provided. Using these
plots, verify that all of the regression assumptions are met.

e) Comment on the overall adequacy of the linear model that we built.

f) What is my projected Relationship Satisfaction Score, and do I have a
shot at a good relationship?

Data Set