Regression Analysis Problems: Statistics Assignment - Fall 2024

This document presents solutions to a regression assignment involving two distinct problems. The first problem focuses on calculating regression between IQ scores of identical twins, including the calculation of standard deviations, means, and the regression equation to predict one twin's IQ based on the other's. It also involves using a web regression applet to establish the regression line and includes a screenshot of the graph. The second problem analyzes the relationship between weight categories and income for a group of women professionals, calculating regression to predict income based on weight category. Similar to the first problem, it includes calculations, the regression equation, and a screenshot from the regression applet. Both problems require detailed calculations and interpretations of regression analysis, demonstrating a comprehensive understanding of statistical concepts.

Regression Assignment
You are presented with 2 regression problems to calculate below. These problems are a
continuation of your correlation problems from the week before. Be sure to fill in
everything. Use your correlation and regression guide and example problem to help you
with your assignment. Remember to show your work!
Problem #1:
IQ scores are determined for eight pairs of identical twins. From the following data,
calculate regression between the scores.
Regression
X Y
s = Σx2 – (Σx)2
n __
n – 1
s= 79057 – (616225)
8__
8 – 1
s = 79057 – 77028.13
__
7
s = 2028.875
__
7
S = 17.02467
s = Σy2 – (Σy)2
n __
n - 1
s= 79428 – (617796)
8__
8 – 1
s = 79428 – 77224.5
__
7
s = 2203.5
__
7
S = 17.7422
Mx = ∑xx/n = 785/8 = 98.125 My = ∑xy/n = 786/8 = 98.25
b = r (sy / sx) = 0.86( 17.7422/17.02467) = 0.86 (1.042147) = 0.896246
Syllabus Page 1 of 4

a = My - (b) (Mx)
= 98.25-0.896246 (98.125)
= 98.25-87.94416
= 10.30584
What would Twin B’s IQ probably be if Twin A’s IQ were 100?
Ŷ = bx + a (where x = 100) = 0.896246 (100) + 10.30584 = 99.93046
Go to the web regression applet: http://www.shodor.org/interactivate/activities/Regression/ and follow the steps in
your assignment guide to establish the regression line. Make a screenshot of the graph and attach to the assignment
here.
Problem #2:
A study was done to compare weight and income for a group of women professionals. The
women were classified into one of five categories for weight: 1 = thinnest to 5 = heaviest.
Income figures are annual income (in thousands), rounded to the nearest $1,000.
Syllabus Page 2 of 4

Regression
X Y
s = Σx2 – (Σx)2
n __
n – 1
s= 110 – (900)
10 __
10 – 1
s = 110 – 90
__
9
s = 20
__
9
= 1.4907
s = Σy2 – (Σy)2
n __
n - 1
s= 50990 – (435600)
10 __
10 – 1
s = 50990 – 43560
__
9
s = 7430
__
9
= 28.73248
Mx = ∑xx/n = 30/ 10 = 3 My = ∑xy/n = 660/10 = 66
b = r (sy / sx)
= (-0.93) (28.73248/1.4907) = (-0.93) (19.27449) = -17.92528
a = My - (b) (Mx)
= 66- (-17.92528) 3
= 66+ 53.77583
Syllabus Page 3 of 4

= 119.7758
If the weight category is 4 what would the income be?
Ŷ = bx + a (where x = 4) = (-17.92528) (4) +119.7758 = -71.7011+ 119.7758 =
48.07472
Go to the web regression applet: http://www.shodor.org/interactivate/activities/Regression/ and follow the steps from
the assignment guide to identify the regression line. Make a screenshot of the graph and attach to the assignment
here.
Syllabus Page 4 of 4