Statistical Analysis: Correlation and Regression Problem Answers

This document presents a comprehensive set of solutions to problems related to correlation and regression in statistics. It covers various aspects, including hypothesis testing, interpretation of correlation coefficients, and the use of regression equations for predictions. The solutions address questions involving scatterplots, null and alternative hypotheses, test statistics, and p-values. The assignment explores the relationship between different variables, such as weights and chest sizes of bears, paper and glass garbage weights, internet users and scientific award winners, and movie budgets and gross revenues. The document includes calculations of predicted values based on regression equations and assesses the significance of correlations at different alpha levels. Overall, the assignment provides a detailed analysis of statistical concepts and their application in real-world scenarios.

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Problems in Statistics – Correlation and Regression

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Answer 1
H0: ρ = 0 (1): There was no linear relation between weights and chest size of wild
bears.
H1: ρ ≠ 0 (2): There was significant linear correlation between weights and chest size
of wild bears.
r = 0.964
B. Critical r = ± 0.268
B.
A.
Answer 2
H0: ρ = 0 (1): There was no linear relation between weights of paper and glass
garbage.
H1: ρ ≠ 0 (2): There was a significant linear correlation weight of paper and glass
garbage.
r = 0.126
B. One critical value at r = 0.126
(1) =
(2) >
(3) Less than or equal to
(4) Is not

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Answer 3
a. D.
b. r = 0.816
C. There is sufficient evidence to support the claim of a linear correlation between the
two variables.
c. B.
Answer 4
a. A
b. r = 0.816
D.
c. D.
Answer 5
Correct Scatterplot D.
Linear correlation r = 0.770
H0: ρ = 0 (1): There was no linear relation between number of internet users and scientific
award winners.
H0: ρ > 0 (2): There was significantly positive linear relation between number of internet
users and scientific award winners.
The P-value = 0.073
(3) Greater than
(4) is not

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Answer 6
Null and alternate hypotheses: A
Scatterplot: A
Correlation coefficient: r = 0.846
Test statistic: t = 4.191
The P-value = 0.004
(1) less
(2) is
Based on results: B
Answer 7
Scatterplot: D
Linear correlation coefficient: r = 0.444
H0: ρ = 0 (1)
H0: ρ ≠ 0 (2)
Test statistic: t = 0.86
P-value = 0.453
(3) greater than
(4) is not

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Answer 8
Null and alternate: C
Scatterplot: D
r = - 0.972
t-stat = - 7.216
P-value = 0.005
(1) less
(2) is
Results suggest: A
Answer 9
Scatterplot: C
r = 0.294
H0: ρ = 0 (1)
H0: ρ ≠ 0 (2)
t-stat = 1.065
P-value = 0.308
(3) greater than
(4) is not
Results suggest: C

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Answer 10
Scatterplot: D
r = 0.710
H0: ρ = 0 (1)
H0: ρ > 0 (2)
t-stat = 4.63
P-value = 0.000
(3) less than or equal to
(4) is
Results suggest: C
Answer 11
Scatterplot: D
r = 0.282
H0: ρ = 0 (1)
H0: ρ ≠ 0 (2)
t-stat = 1.21
P-value = 0.243
(5) greater than
(6) is not

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Answer 12
Scatterplot: D
r = 0.368
H0: ρ = 0 (1)
H0: ρ > 0 (2)
t-stat = 2.91
P-value = 0.005
(7) less than or equal to
(8) is
Answer 13
Predicted Y
^¿
¿ = 5.9 (Mean) as there is no significant correlation
Answer 14
Predicted Y
^¿
¿ = -5.78 + 1.06 * 95 = 94.92, as correlation is significant at alpha = 0.05
Answer 15
Predicted Y
^¿
¿ = 81.48 kg (Mean) as there is no significant correlation at alpha = 0.01.
Answer 16
Regression equation: Y
^¿
¿ = -229.6 + Chest size * 10.2

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Predicted weight: Y
^¿
¿ = -229.6 + 43 * 10.2 = 209.0 pounds for 43 inches chest sized bear.
Is the result close? : D
Answer 17
Regression equation: Y
^¿
¿ = 60.7 + Right * 1.1
Predicted left arm blood pressure: Y
^¿
¿ = 158.2 mmHg (Mean) as there is no significant
correlation at alpha = 0.05.
Answer 18
Regression equation: Y
^¿
¿ = 16.511 - 0.003 * Lemon Imports
Predicted crash fatality rate: Y
^¿
¿ = 16.511 - 0.003 * 525 = 15.2 per 100,000 people, as the
correlation is significant at alpha = 0.05.
Is prediction worthwhile? : B
Answer 19
Regression equation: Y
^¿
¿ = 51.1 - 0.156 * Actress
Predicted age of best actor: Y
^¿
¿ = 45 years (Mean) for 31 year actress, as the correlation is not
significant at alpha = 0.05.
Is result within 5 years? : (1) No, (2) more than 5 years less than

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Answer 20
Regression equation: Y
^¿
¿ = 4.983 - 0.010 * Salary
Best predicted number of viewers: Y
^¿
¿ = 4.8 million (Mean) for salary of $ 3 million, as the
correlation is not significant at alpha = 0.05.
Is result close to 2 million? : B.
Answer 21
Regression equation: Y
^¿
¿ = 0.00037 + 3.14077 * Diameter
Best predicted number of viewers: Y
^¿
¿ = 0.00037 – 3.14077 * 1.5 = 4.71 cm, as the correlation
between the variables is significant at alpha = 0.05.
Is result close to 4.7 cm? : B.
Answer 22
Regression equation: Y
^¿
¿ = - 23.4 + 0.459 * Internet users per 100
Best predicted number of Nobel laureates: Y
^¿
¿ = - 23.4 + 0.459 * 79.9 = 13.2 per 10 million, as
the correlation between the variables are significant at alpha = 0.05.
Is result close to 1.4 per 10 million? : C.

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Answer 23
Regression equation: Y
^¿
¿ = 19.9 + 1.3 * Budget
Best predicted gross for a movie: Y
^¿
¿ = 19.9 + 1.3 * 100 = $ 149.9 million, as the correlation
between the variables are significant at alpha = 0.05.