Question 1 A researcher did a study to investigate the potential… Question 1A 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-05b1 for Age 2.1927 0.6025 3.639 0.00541Residual standard error: 5.552 on 9 degrees of freedomMultiple R-squared: 0.5954, Adjusted R-squared: 0.5505Did a linear relationship exist between Age (independent) and DBP?Group of answer choicesa) 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 2A 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-05b1 for Age 2.1927 0.6025 3.639 0.00541Residual standard error: 5.552 on 9 degrees of freedomMultiple R-squared: 0.5954, Adjusted R-squared: 0.5505What was the linear regression equation from the above analysis?Group of answer choicesA. DSP hat = 2.1927*AgeB. DSP hat = 49.8844 *AgeC. DSP hat = 49.8844 + 2.1927*AgeD. DSP hat = 2.1927 + 49.8844*AgeQuestion 3A 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-05b1 for Age 2.1927 0.6025 3.639 0.00541Residual standard error: 5.552 on 9 degrees of freedomMultiple R-squared: 0.5954, Adjusted R-squared: 0.5505What was the correlation coefficient between Age and DBP? [In regard to rounding, choose the answer “closest” to your calculation result]Group of answer choicesA. r cannot be decided based on the information provided.B. r = 2.1927C. r = – 0.77D. r = 0.77Question 4A 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-05b1 for Age 2.1927 0.6025 3.639 0.00541Residual standard error: 5.552 on 9 degrees of freedomMultiple R-squared: 0.5954, Adjusted R-squared: 0.5505Based on the correlation coefficient, how do you describe the linear relationship between Age and DBP using the conventional classification?Group of answer choicesA. Not enough information to make any statementB. Positive, strong linear relationship;C. Negative, strong linear relationshipD. Positive, weak linear relationshipQuestion 5A 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-05b1 for Age 2.1927 0.6025 3.639 0.00541Residual standard error: 5.552 on 9 degrees of freedomMultiple R-squared: 0.5954, Adjusted R-squared: 0.5505Based 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 choicesA. 69.6B. 76.4C. 53.2D. Cannot be decided.Question 6A 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-05b1 for Age 2.1927 0.6025 3.639 0.00541Residual standard error: 5.552 on 9 degrees of freedomMultiple R-squared: 0.5954, Adjusted R-squared: 0.5505Based 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 choices04.3949.882.19Question 7A 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 0.03186b1 for Age 0.8614 0.2482 3.470 0.00844b2 for Weight 0.3349 0.1307 2.563 0.03351Residual standard error: 2.318 on 8 degrees of freedomMultiple 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 choicesA. No linear relationship existed between Age and SBP nor between Weight and SBPB. A linear relationship only existed between Age and SBPC. Both Age and Weight were linearly associated with SBP.D. None of the above answers.Question 8A 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 0.03186b1 for Age 0.8614 0.2482 3.470 0.00844b2 for Weight 0.3349 0.1307 2.563 0.03351Residual standard error: 2.318 on 8 degrees of freedomMultiple 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 choicesA. 100%B. 97%C. 3%D. Not enough information to make a decisionQuestion 9A Pearson’s correlation coefficient r < 0 indicates no relationship between the independent variable X and the dependent variable Y.Group of answer choicesTrueFalseQuestion 10A 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 choicesTrueFalseMathStatistics and Probability BIOSTAT PHR 7784
