Question

A jeweler prices diamonds on the basis of quality (with values from 0 to 8, with 8 being flawless and 0 containing numerous imperfections) and color (with values from 1 to 10, with 10 being pure white and 1 being yellow). Based on the price per carat (in hundreds of dollars) of the following 11 diamonds of approximately the same weight, determine the relationship between quality (X1), color (X2) and price (Y).

Color Quality Price

7 5 65

3 7 38

5 8 51

8 1 38

9 3 55

5 4 43

4 0 25

2 6 33

8 7 71

6 4 51

9 2 49

1)Identify the correlation coefficient and the coefficient of interpretation, and comment on the strength of the linear relationship (very strong, strong, somewhat strong, not strong)

2) Determine the regression equation

3) Make one prediction of the dependent variable, y, by substituting values into the independent variables, x

4) Identify the result of the test for significance of the regression equation

Answer #1

1) The karl pearson correlation coefficient is

The relation between Color and price is 0.625

The relation between Color and Quality is -0.334

The relation between price and quality is 0.431

2)

The regression equation is

Price = 1.75 + 4.90 Color + 3.76 Quality

3) The output from MINITAB is

The p-value of color and quality is less than alpha 0.05 There the both variables are significant

4) P-value of regression is 0.000 < alpha 0.05 so we reject H0

Thus we conclude that the regression is best fit to the given data

The data table found below contains the listed prices and
weights of the diamonds in 20 rings offered for sale in a newspaper
in a foreign city. The prices are in local dollars with the weights
in carats. Complete parts (a) through (g) below.
Weight (carats)
Price (dollars)
0.13
224
0.22
578
0.24
649
0.12
229
0.3
895
0.38
1155
0.24
624
0.28
781
0.14
270
0.25
628
0.21
514
0.14
275
0.25
640
0.39
1239
0.3
831
0.12
191...

The table below shows the income for an employee over his first
8 years of work. Use this to estimate
his income for his 15th year of work.
Years
1
2
3
4
5
6
7
8
Income
45,000
46,814
48,212
52,870
54,125
58,532
61,075
62,785
Linear Regression Equation: ____________________
Correlation Coefficient (r): _________
Type of Correlation: ______________________
Is the correlation strong? Explain
Using the linear regression equation predict
his income for his 15th year of work.

1. The quality of coffee is to be gauged by two coffee
tasters. They apply a rating from 0 to 10 (with good coffee rated
10, poor coffee rated 0). The coffee has been perked from 1 to 8
minutes. The regression equation is y=1.01x-.55. What taste value
do you expect for coffee perked 5 minutes, 7 minutes, 11
minutes?
2. Is there a correlation between the minutes the
coffee is perked and the taste value? There were 16 pairs...

A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
portion of the data is as follows:
Salary
Education
40
3
53
4
⋮
⋮
38
0
Salary
Education
40
3
53
4
80
6
42
2
70
5
50
4
110
8
38
0
42
3
55
4
85
6
40
2
70
5
60
4
140
8
40
0...

A social scientist would like to analyze the relationship
between educational attainment (in years of higher education) and
annual salary (in $1,000s). He collects data on 20 individuals. A
portion of the data is as follows:
Salary
Education
42
6
48
7
82
1
46
3
67
1
54
5
105
6
42
0
38
4
56
6
90
2
44
7
67
5
64
7
143
12
43
0
76
7
64
4
127
6
42
0
a. Find...

Simple regression analysis
The following data were collected to study the relationship between
the sale price, y and the total appraised value, x, of a
residential property located in an upscale neighborhood.
Property
x
y
x2
y2
xy
1
2
2
4
4
4
2
3
5
9
25
15
3
4
7
16
49
28
4
5
10
25
100
50
5
6
11
36
121
66
Draw a scatter diagram of the sale price and the total appraised...

A new set of measurements are obtained with the values 0, 1,2,
3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and these values are found 0, 1, 2,
3, 4, 5, 6, 5, 4, 3, 2, 1, 0 times, respectively. Find the the
average value of the measurements and the statistical uncertainty
based on the measurements.

One of the biggest changes in higher education in recent years
has been the growth of online universities. The Online Education
Database is an independent organization whose mission is to build a
comprehensive list of the top accredited online colleges. The
following table shows the retention rate (%) and the graduation
rate (%) for 29 online colleges. Retention Rate (%) Graduation Rate
(%) 7 25 51 25 4 28 29 32 33 33 47 33 63 34 45 36 60...

NOTE: you might be able to get all the necessary information
from the Excel analysis output or the scatter plot. You don’t need
to do computations by applying the numeric formula.
A clothing department wants to find out if there is a
relationship (and what kind of relationship) between the price of
an item and the time that it takes to a customer to decide in
buying that item.
ITEM PRICE (X)
DECISION TIME IN MINUTES (Y)
$17
9
$63...

Find the equation of the regression line for the given data.
Round values to the nearest thousandth.
x
y
−5
−10
−3
−8
4
9
1
1
−1
−2
−2
−6
0
−1
2
3
3
6
−4
−8
._____________________
A. y=0.522x−2.097
B. y=−0.552x+2.097
C. y=2.097x+0.552
D. y=2.097x−0.552

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