Statistics and Probability Answers

orrelation

The following are data for 12 individuals’ daily sodium intake and their systolic blood pressure readings. A research investigator is interested in learning how strong the association is between these variables and how well we can predict blood pressure from sodium intake. Test the association at alpha 0.01.

Person


1

2

3

4

5

6

7

8

9

10

11

12



Sodium (X)

6.8

7.0

6.9

7.2

7.3

7.0

7.0

7.5

7.3

7.1

6.5

6.4

BP (Y)

154

167

162

175

190

158

166

195

189

186

148

140





1. Formulate the H0 and H1
2. C. V. at alpha 0.01 level of significance
3. Compute the test value: Pearson r, then t-value
4. Decision
5. Interpretation

A model selection method where we start with an empty model and add variables one at a time until no other important variables are found is called

A. multiple testing
B. bootstrapping
C. randomization
D. ANOVA
E. forward selection

1. Which of the following is the best definition of a parsimonious model?

A. The model with the highest R^2
B. The model that includes all the predictors that your audience is interested in.
C.The model with the most number of predictors.
D.The simplest model with the highest predictive power.

2. A high correlation between two explanatory variables such that the two variables contribute redundant information to the model is known as

A. adjusted R^2
B. homoscedasticity
C. collinearity
D. heteroscedasticity
E. multiple correlation
F. heterogeneity
G. multiple interaction
H. homogeneity

True/False: Outliers should always be removed from the data set prior to final analysis.

A.True; outliers distort model fit and must be removed to assure reliable results.

B. False; we only remove outliers after checking to make sure doing so drastically improves model fit.

C.False; we only remove outliers if we have very good justification that suggests that removing the outlier is appropriate.

Based on an observational study, a clinical psychologist finds that the relationship between the number of weeks spent in a therapy hospital and number of seizures per week is described by the following equation:  

seizures = 14.09-0.91 weeks

Which of the following is the best interpretation of the slope estimate?

A. For each additional seizure per week, we would expect the average number of additional weeks spent in the therapy hospital to be higher by 0.91 seizures.

B. Each additional week spent in a therapy hospital decreases the number of seizures per week by 0.91.

C. For each additional week spent in the therapy hospital, we would expect the average number of seizures per week to lower by 0.91 seizures.

D. All patients start their treatment with at least 14.09 seizures per week.

1. Which of the following best describes SST (sum of squares total) in a regression?

A. Strength of the model fit.
B. Total variability in the explanatory variable.
C. Unexplained variability in the response variable.
D. Total variability in the response variable.


Explained variability in the response variable.
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1. A colleague needs some help with a statistics problem: He brings you the plot shown below, along with a correlation coefficient of 0.03 which he calculated himself. The plot shows two numerical variables which are obviously strongly related, and as a result your colleague is afraid he made a mistake calculating the correlation coefficient: that is, he was surprised to get an answer so close to 0. Given only this information, which of the following responses is the best to give your colleague?

A. The correlation coefficient measures the strength of the linear relationship, therefore two variables that have a strong non-linear association might still have a low correlation coefficient.

B. Your colleague must have made a mistake in his calculations. A much higher correlation coefficient is expected for variables that show a clear association.

2. Fill in the blanks: A data point that has a negative residual is located ________ the regression line.

A. above
B. on
C. below

For a certain professional basketball team, 32% of the variability in the team’s points scored per game is explained by the total salary of the opposing team. For this particular team, which of the following could be the correlation between their points scored per game and the salary of the opposing team?

A. 1 - Square root of o.32 = 0.434
B. 1- 0.32^2 = 0.998
C.- square root of 0.32 = -0.566
D. - 0.32^2 = -0.102

Sixteen student volunteers at Ohio State University drank a randomly assigned number beers. Thirty minutes later, a police officer measured their blood alcohol content (BAC) in grams of alcohol per deciliter of blood. The scatterplot displays the relationship between BAC and number of beers consumed. Suppose a mistake was found in the data: the student who supposedly drank the highest number of beers (9 beers) actually only drank 6. His BAC was recorded correctly. In a new scatterplot, how would the strength of the association appear - compared to the strength of the association shown here?

A. Roughly the same as the strength of the association shown in the above scatter plot
B. Weaker than the strength of the association shown in the above scatter plot
C. Stronger than the strength of the association shown in the above scatter plot
D. It is impossible to tell

Which of the following is false?

A.The variability of residuals should increase as x increases.
B. Residuals of linear models should be distributed nearly normally around 0.
C. The residuals plot (residuals vs. x) should show a random scatter around 0.
D. A data point that has negative residual is located below the regression line