Statistics Final Exam

What are a few properties of the correlation coefficient?

1. The correlation coefficient does not change the measurement scale. 2. The sign of the correlation coefficient is the same as the covariance. 3. The linear correlation coefficient is a real number between −1 and 1.

A regression between foot length (response variable in cm) and height (explanatory variable in inches) for 33 students resulted in the following regression equation of Foot Length = 10.9 + (0.23)(Height). One student in the sample was 73 inches tall with a foot length of 29 cm. What is the residual for this student? 29 cm 1.31 cm 0.00 cm -1.31 cm

1.31

Which one of the following is not appropriate for studying the relationship between two quantitative variables? Scatterplot Bar chart Correlation Regression

Bar chart

Which one of the following choices describes a problem for which an analysis of variance would be appropriate? Comparing the proportion of successes for three different treatments of anxiety. Each treatment is tried on 100 patients. Analyzing the relationship between high school GPA and college GPA. Comparing the mean birth weights of newborn babies for three different racial groups. Analyzing the relationship between gender and opinion about capital punishment (favor or oppose).

Comparing the mean birth weights of newborn babies for three different racial groups.

Which of the following cannot be answered from a regression equation? Predict the value of y at a particular value of x. Estimate the slope between y and x. Estimate whether the linear association is positive or negative. Estimate whether the association is linear or non-linear.

Estimate whether the association is linear or non-linear.

What is a regression analysis

Examines the relationship between quantitative response (y) and explanatory (x) variables

Large Residual

Indicates an unusual observation

Statistical Relationship

Known values for one variable can be used to determine the average value of the other variable where there is variation from the average pattern

Deterministic Relationship

Known values for one variable can be used to determine the exact value of the other variable

What does it mean when the correlation is 0?

No relationship Horizontal line

Extrapolation

Predicting outside of the range of x riskier the farther_ we move from the range of the given x-values • no guarantee that the relationship given by the regression equation holds outside the range of sampled x-values

The correlation between two variables is given by r = 0.0. What does this mean? The best straight line through the data is horizontal at the mean of y. There is a perfect positive relationship between the two variables There is a perfect negative relationship between the two variables. All of the points must fall exactly on a horizontal straight line.

The best straight line through the data is horizontal at the mean of y.

Which one of the following statements involving correlation is possible and reasonable? The correlation between hair color and eye color is 0.80. The correlation between the height of a father and the height of his first son is 0.6 The correlation between left foot length and right foot length is 2.35. The correlation between hair color and age is positive.

The correlation between the height of a father and the height of his first son is 0.6

Residual

The difference between the observed y-value and the predicted value y-hat

Which of the following is not one of the assumptions made in the analysis of variance? Each sample is an independent random sample. The distribution of the response variable is a normal curve within each population. The different populations all have the same mean. The different populations all have the same standard deviation σ.

The different populations all have the same mean.

Ninety people with high cholesterol are randomly divided into three groups of thirty, and a different treatment program for decreasing cholesterol is assigned to each group. The response variable is the change in cholesterol level after two months of treatment. An analysis of variance will be used to compare the three treatments. What null hypothesis is tested by this F-test? The sample variances are equal for the three treatment groups. The population variances are equal for the three treatments. The sample means are equal for the three treatment groups. The population means are equal for the three treatments.

The population means are equal for the three treatments.

The value of a correlation is reported by a researcher to be r = -0.5. Which of the following statements is correct? The x-variable explains 50% of the variability in the y-variable. The x-variable explains -50% of the variability in the y-variable. The x-variable explains 25% of the variability in the y-variable. The x-variable explains -25% of the variability in the y-variable.

The x-variable explains 25% of the variability in the y-variable.

What is the regression line? How is it used?

When the best equation for describing the relationship between x and y is a straight line, the equation is called the regression line predicts the value for the response variable y as a straight-line function of the values of the explanatory variable x

Restricted Range

arises when the range between the lowest and highest scores on one or both variables is limited • will reduce the accuracy of the correlation coefficient

What is a regression equation

describes the average relationship between x and y variables

Outliers in the x direction

meaning that the removal of such points would markedly change the equation of the line tend to pull the regression line to that data point and farther from the rest of the data

What does a correlation measure?

measures the direction and the strength of the linear relationship between two quantitative variables

What does it mean when the correlation is -1.00?

perfect negative linear relationship

What does it mean when the correlation is +1.00?

perfect positive linear relationship

What is regression analysis?

regression analysis is a statistical process for estimating the relationships among variables.

A scatter plot and regression line can be used for all of the following except to determine if any (x, y) pairs are outliers. to predict y at a specific value of x. to estimate the average y at a specific value of x. to determine if a change in x causes a change in y.

to determine if a change in x causes a change in y.

Least squares regression line

the line that minimizes the vertical distance between the points and their predictions

When multiple tests are done in analysis of variance, the family error rate is the smallest P-value among the tests in the set. the probability of making one or more Type II errors among the tests. the probability of not rejecting the null hypothesis when the null hypothesis is true. the probability of making one or more Type I errors among the tests

the probability of making one or more Type I errors among the tests.

Small Residual

the smaller the absolute value of a residual, the closer the predicted value is to the actual value

what is Simple Linear Regression

used to analyze the relationships between one quantitative x variable and one quantitative y variable

Simpsons Paradox

when the direction of an association between two variables changes after we include a third variable and analyze the data at separate levels of that third variable

Sum of Residual

will always be 0