Question 1

A researcher did a study to investigate the potential relationship between diastolic blood pressure (DBP, dependent variable) and age (independent variable) for boys 5 to 13 years old. The data were analyzed using a simple linear regression model and the statistical results were as following.

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 49. 8844 5.7272 8.710 1.12e-05

b1 for Age 2.1927 0.6025 3.639 0.00541

Residual standard error: 5.552 on 9 degrees of freedom

Multiple R-squared: 0.5954, Adjusted R-squared: 0.5505

Did a linear relationship exist between Age (independent) and DBP?

Group of answer choices

a) Statistical analyses showed b1 was significantly different from 0 (p = 0.00541) so there existed a linear relationship between Age (independent) and DBP(dependent).

b) Statistical analyses showed b0 was significantly different from 0 (p = 1.12e-5) so there existed a linear relationship between Age (independent) and DBP.

c) There was no a linear relationship between Age (independent) and DBP because b1 was too small compared with b0.

d) There is not enough information to make a decision.

Question 2

A researcher did a study to investigate the potential relationship between diastolic blood pressure (DBP, dependent variable) and age (independent variable) for boys 5 to 13 years old. The data were analyzed using a simple linear regression model and the statistical results were as following.

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 49. 8844 5.7272 8.710 1.12e-05

b1 for Age 2.1927 0.6025 3.639 0.00541

Residual standard error: 5.552 on 9 degrees of freedom

Multiple R-squared: 0.5954, Adjusted R-squared: 0.5505

What was the linear regression equation from the above analysis?

Group of answer choices

A. DSP hat = 2.1927*Age

B. DSP hat = 49.8844 *Age

C. DSP hat = 49.8844 + 2.1927*Age

D. DSP hat = 2.1927 + 49.8844*Age

Question 3

A researcher did a study to investigate the potential relationship between diastolic blood pressure (DBP, dependent variable) and age (independent variable) for boys 5 to 13 years old. The data were analyzed using a simple linear regression model and the statistical results were as following.

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 49.8844 5.7272 8.710 1.12e-05

b1 for Age 2.1927 0.6025 3.639 0.00541

Residual standard error: 5.552 on 9 degrees of freedom

Multiple R-squared: 0.5954, Adjusted R-squared: 0.5505

What was the correlation coefficient between Age and DBP? [In regard to rounding, choose the answer "closest" to your calculation result]

Group of answer choices

A. r cannot be decided based on the information provided.

B. r = 2.1927

C. r = - 0.77

D. r = 0.77

Question 4

A researcher did a study to investigate the potential relationship between diastolic blood pressure (DBP, dependent variable) and age (independent variable) for boys 5 to 13 years old. The data were analyzed using a simple linear regression model and the statistical results were as following.

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 49.8844 5.7272 8.710 1.12e-05

b1 for Age 2.1927 0.6025 3.639 \ 0.00541

Residual standard error: 5.552 on 9 degrees of freedom

Multiple R-squared: 0.5954, Adjusted R-squared: 0.5505

Based on the correlation coefficient, how do you describe the linear relationship between Age and DBP using the conventional classification?

Group of answer choices

A. Not enough information to make any statement

B. Positive, strong linear relationship;

C. Negative, strong linear relationship

D. Positive, weak linear relationship

Question 5

A researcher did a study to investigate the potential relationship between diastolic blood pressure (DBP, dependent variable) and age (independent variable) for boys 5 to 13 years old. The data were analyzed using a simple linear regression model and the statistical results were as following.

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 49.8844 5.7272 8.710 1.12e-05

b1 for Age 2.1927 0.6025 3.639 0.00541

Residual standard error: 5.552 on 9 degrees of freedom

Multiple R-squared: 0.5954, Adjusted R-squared: 0.5505

Based on the statistical results, what would be the expected DSP value for a boy at the age of 9? [In regard to rounding, choose the answer "closest" to your calculation result]

Group of answer choices

A. 69.6

B. 76.4

C. 53.2

D. Cannot be decided.

Question 6

A researcher did a study to investigate the potential relationship between diastolic blood pressure (DBP, dependent variable) and age (independent variable) for boys 5 to 13 years old. The data were analyzed using a simple linear regression model and the statistical results were as following.

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 49.8844 5.7272 8.710 1.12e-05

b1 for Age 2.1927 0.6025 3.639 0.00541

Residual standard error: 5.552 on 9 degrees of freedom

Multiple R-squared: 0.5954, Adjusted R-squared: 0.5505

Based on the statistical results, what would be the expected difference in DSP between a boy at 10 and a boy at 12? [In regard to rounding, choose the answer "closest" to your calculation result]

Group of answer choices

0

4.39

49.88

2.19

Question 7

A researcher intended to investigate the potential associations between systolic blood pressure (SBP, the dependent variable) (mmHg) and two independent variables Age (year) and Weight (pound). He used a multiple linear regression model to analyze the data. The results from statistical analyses are following:

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 30.9941 11.9438 2.595 0.03186

b1 for Age 0.8614 0.2482 3.470 0.00844

b2 for Weight 0.3349 0.1307 2.563 0.03351

Residual standard error: 2.318 on 8 degrees of freedom

Multiple R-squared: 0.9768, Adjusted R-squared: 0.9711

What statement can you make about the relationships between SBP and Age, between SBP and Weight?

Group of answer choices

A. No linear relationship existed between Age and SBP nor between Weight and SBP

B. A linear relationship only existed between Age and SBP

C. Both Age and Weight were linearly associated with SBP.

D. None of the above answers.

Question 8

A researcher intended to investigate the potential associations between systolic blood pressure (SBP, the dependent variable) (mmHg) and two independent variables Age (year) and Weight (pound). He used a multiple linear regression model to analyze the data. The results from statistical analyses are following:

Estimate Std. Error t value Pr(>|t|)

b0 (Intercept) 30.9941 11.9438 2.595 0.03186

b1 for Age 0.8614 0.2482 3.470 0.00844

b2 for Weight 0.3349 0.1307 2.563 0.03351

Residual standard error: 2.318 on 8 degrees of freedom

Multiple R-squared: 0.9768, Adjusted R-squared: 0.9711

How many percentage of variance in SBP can be explained by the linear model including Age and Weight?

Group of answer choices

A. 100%

B. 97%

C. 3%

D. Not enough information to make a decision

Question 9

A Pearson's correlation coefficient r < 0 indicates no relationship between the independent variable X and the dependent variable Y.

Group of answer choices

True

False

Question 10

A linear regression equation and multiple linear regression equations can be used to calculate true (exact) Y for a specific individual, such as my classmate Joe Known if all the x values of Joe Known are given.

Group of answer choices

True

False