Question

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 |
15 |

$140 |
20 |

$250 |
30 |

$10 |
4 |

$8 |
5 |

$170 |
27 |

$280 |
30 |

- Using Excel construct a scatter plot. Discuss the output of the scatter plot.
- Give (or calculate) the correlation coefficient.
- Give (or calculate) the coefficient of determination.
- Give (or calculate) the regression equation coefficients; Give the equation of regression.

**e. (very important)**

Based on the above values, in detail draw the conclusion:

- Discuss the correlation coefficient r
- Discuss the coefficient of determination r
^{2} - Discuss in detail the meaning of the regression equation

**f. (unrelated to previous data)**

A company has a set of data with employee age (X) and the corresponding number of annual on-the-job-accidents.

Analysis on the set finds that the regression equation is Y= 110-3.78X.

- What can be said of the correspondence between age and accidents?
- Are younger workers safer or more prone to accident?
- What is the likely number of accidents for someone of 23 years old?

Answer #1

Shown below is a portion of an Excel output for regression
analysis relating Y (dependent variable) and X (independent
variable).
ANOVA
df
SS
Regression
1
39947.80
Residual (Error)
10
8280.81
Total
11
48228.61
Coefficients
Standard Error
t Stat
P-value
Intercept
69.190
26.934
2.569
0.02795
X
2.441
0.351
6.946
0.00004
1. What is the estimated regression equation
that relates Y to X?
2. Is the regression relationship significant?
Use the p-value approach and alpha = 0.05 to answer this
question.
3. What is the...

Shown below is a portion of an Excel
output for regression analysis relating Y (dependent variable) and
X (independent variable).
ANOVA
df
SS
Regression
1
3348.312
Residual
8
9529.811
Total
9
12878.123
Coefficients
Standard Error
t Stat
P-value
Intercept
247.56
83.280
1.689
0.030
X
148.62
38.312
1.283
0.075
1. What is the estimated regression equation that relates y to x?
(2 Points)
2. Is the regression relationship significant? Use a p-value and
alpha = 0.05. (2 Points)
3. What is...

The following output was obtained from a regression analysis of
the dependent variable Rating and an independent variable Price.
(10 points)
ANOVA
df
SS
MS
F
Regression
1
372.707
372.707
42.927
Residual
15
130.234
8.682
Total
16
502.941
Coefficients
Standard Error
t Stat
P-value
Intercept
45.623
3.630
12.569
0.000
Price
0.107
0.016
6.552
0.000
Use the critical value approach to perform an F test for the
significance of the linear relationship between Rating and Price at
the 0.05 level of...

Homework 4 Question 2 A large school district is reevaluating
its teachers' salaries. They have decided to use regression
analysis to predict mean teacher salaries at each elementary
school. The researcher uses years of experience to predict salary.
The resulting equation was: where Y = salary and X = years of
experience. The raw data is given in the table below.
Salary Years of experience
$54,000.00 13
$42,140.00 9
$36,195.00 7
$45,000.00 9
$58,950.00 14
$56,890.00 13
$53,250.00 14
$49,800.00...

1. The following output was obtained from a regression
analysis of the dependent variable Rating and an independent
variable
Price.
Anova
df SS MS f
Regression 1 301.701 301.701 32.94
Residual 15 128.221 9.1586
Total 16 429.922
Coefficients Standard Error T Stat P value
Intercept 45.623 3.630 12.569 0.000
Price .107 0.016 6.552 0.002
a. Use the critical value approach to perform an F test for the
significance of the linear relationship between Rating and Price at
the 0.05 level...

12.4 Study the following Minitab output from a regression analysis
to predict y from x.
a. What is the equation of the regression
model?
b. What is the meaning of the coefficient of
x?
c. What is the result of the test of the slope of
the regression model? Let α = .10.Why is the t ratio
negative?
d. Comment on r2 and the
standard error of the estimate.
e. Comment on the relationship of the F
value to the...

1. Regression analysis is to be conducted with data
from vegetarians to see whether the number of grams of protein each
ate per day was related to diastolic blood pressure.
The resulting regression formula will be used by medical personnel
to predict blood pressure in a weight loss clinic in downtown
Pittsburgh.
Subject
Grams of protein
Diastolic BP
1
4
73
2
6.5
79
3
5
83
4
5.5
82
5
8
84
6
10
92
7
9
88
8...

Regression analysis is to be conducted with data from
vegetarians to see whether the number of grams of protein each ate
per day was related to diastolic blood pressure. The resulting
regression formula will be used by medical personnel to predict
blood pressure in a weight loss clinic in downtown
Pittsburgh.
Subject
Grams of protein
Diastolic BP
1
4
73
2
6.5
79
3
5
83
4
5.5
82
5
8
84
6
10
92
7
9
88
8
8.2...

A hypothesis test using a Pearson’s correlation coefficient is
an example of what?
A nonparametric statistic
A descriptive statistic
An inferential statistic
A power statistic
1 points
QUESTION 48
What would the scatter plot show for data that produce a Pearson
correlation of r = +0.88?
Points clustered close to a line that slopes down to the
right
Points clustered close to a line that slopes up to the right
Points widely scattered around a line that slopes up...

Applications I
Consider the following data representing the total time (in hours)
a student spent on reviewing for the Stat final exam and the actual
score on the final. The sample of 10 students was taken from a
class and the following answers were reported.
time score
0 23
4 30
5 32
7 50
8 45
10 55
12 60
15 70
18 80
20 100
Part 1: Use the formulas provided on the 3rd formula sheet to
compute...

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