correlation quiz (2)

All correlation coefficients share in common the property that they range between

+1.00 and -1.00

In a regression analysis, the regression equation is given by Y ^ = 12 − 6 X . If SSE=510 and SST=1000, then the coefficient of correlation is:

-0.7

Many measures of association have a lower limit of _____ and an upper limit of _____.

-1, +1

The following results were obtained from a simple regression analysis: Y ^ = 37.2895 − 1.2024 XR2 = 0.6744s2 = 0.2934For each unit change in the independent variable X, the estimated change in the mean value of the dependent variable Y is equal to:

-1.2024

The relationship between number of beers consumed (X) and blood alcohol content (Y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: \hat Y = - 0.0127 + 0.0180X.

.0027 below the legal limit

What is the correlation between the following z-scores? (XY 1.3 1.6 -1.2 -1.0 -0.1 -0.2 0.5 0.3 -0.8 -0.6)

.97

If height is independent of average yearly income, what is the predicted correlation between these two variables?

0

In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination (R2) is:

0.6000

If a regression equation is Y ^ = 1.7 + .3 X where Y represents the number of words correctly identified on a 10-point scale and X represents the number of years of education. How many years of education are associated with an average vocabulary score of 6.5?

16

If a regression equation is Y ^ = 1.7 + .3 X where Y represents the number of words correctly identified on a 10-point scale and X represents the number of years of education. What would be the predicted average number of correct words for people with 12 years of education?

5.3

A significant relationship was found between age (in years) and scores on the measure of anxiety (r=.26). What proportion of variance did these two variables share?

6.8%

If the correlation coefficient is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is:

64%

If the correlation coefficient is .90, then the percentage of the variation in the dependent variable Y that is explained by the variation in the independent variable X is:

81%

You believe that there is a weak relationship between your height and the grades you earn in your courses. Which of the following pieces of evidence would support your belief?

A correlation coefficient close to 0.0.

If two variables are highly correlated, what do you know?

Changes in one variable are accompanied by predictable changes in the other

A politician makes the following claim in a speech: "Correlational research has clearly shown that a lack of education causes people to turn to a life of drugs." What is wrong with this politician's claim?

Correlational research does not prove that one variable causes another.

A correlation of -0.5 would indicate a scatterplot in which the slope is:

Downwards

If you read that the slope of a scatterplot is 2.00, what does this mean?

For every increase of 1 on the X -axis there is an increase of 2.00 on the Y -axis

If you read that the slope of a scatterplot is -5, what does this mean?

For every increase of 1 on the X-axis there is a decrease of 5 on the Y-axis.

Which of the following statements about correlation coefficients are true?

I. Correlations are not affected by changes in measurement units of the variables. II. Correlations are not affected by which variable is called X and which variable is called Y.

Suppose that a study finds a correlation relating family income to SAT scores of 0.75. Choose the appropriate conclusions from the following list:

III only (correlation cannot show cause)

The F-statistic for testing the entire regression model can be expressed as:

MSR/MSE

A person does not believe in the adage, "There is safety in numbers." They know that when many people observe an accident, the victim is less likely to receive assistance. They believe that there is a _____ correlation between these variables.

Negative

If pairs of scores occupy the same positions within their own distributions (high w/ high, avg w/ avg, low w/ low)

Pearson's r will be high and positive

For a regression model, the total variation in Y can be expressed as:

SSR + SSE

In order to calculate the coefficient of determination R2, you would use which of the following formulas?

SSR/SST

The correlation coefficient ________

Should be interpreted alongside the relevant scatterplot

All but one of these statements is false. Which one could be true?

The correlation between the amounts of fertilizer used and quantity of beans harvested is .42

What is the statistical decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 9.488 and the computed value is 6.079?

The difference is probably due to sampling error; do not reject the null hypothesis.

A correlation coefficient equal to -0.95 means that:

The relationship between two variables is strong and negative

If the Pearson correlation coefficient r is equal to 1 then:

There is a perfect positive relationship between the two variables.

With a scatterplot, the dependent variable is represented on which axis?

Y

Which of the following would not allow you to calculate a valid correlation?

a curvilinear relationship between X and Y

In a data set, if two variables X and Y have a strong negative correlation, then a scatterplot of their values would fit approximately around:

a straight line going down to the right

Suppose we fitted a least squares regression line and obtained Y ^ = − 4.3 − 1.25 X and R2 = 0.97. Which of the following three statements are true?

about 97% of the variation in Y can be explained by a linear relationship with X

The reject/not reject decision for a hypothesis test in regression:

all of the above

In regression analysis, the variable that is used to explain the change in the outcome measure is called:

all of the above (independent=predictor=explanatory)

In a 2x2 table, if one cell frequency is known:

all other cell frequencies are determined

A student produces a correlation of +1.3. This is:

an impossible correlation

Larger values of R^2 imply that the observations are more closely grouped about the:

average value of the independent variables

In regression analysis, if the independent variable is measured as income in dollars, the dependent variable:

can be any units

If the coefficient of determination is equal to 1, then the coefficient of correlation:

can be either -1 or +1

If the coefficient of determination (R2) is a positive value, then the coefficient of correlation:

can be either negative or positive

The coefficient of determination (R2):

cannot be negative

If social class is a cause of a person's political ideology, then __________ is the independent variable and __________ is dependent.

class, ideology

The strength (degree) of the correlation between an independent variable X and a dependent variable Y is measured by:

correlation coefficient

In regression analysis, the variable that is being predicted is the:

dependent variable

If all the points of a scatterplot lie on the least squares regression line, then the coefficient of determination (R2) for these variables based on this data is:

either 1 or -1, depending upon whether the relationship is positive or negative

Cell frequencies computed under the assumption that the null hypothesis is true are called:

expected frequencies

Suppose a straight line is fitted to data having a dependent variable Y and independent variable X. Predicting values of Y for values of X outside the spread of the observed data is called:

extrapolation

In a negative relationship:

if case A ranks above case B on one variable, it will rank below case B on the other variable

One limitation of the chi-square test (and all hypothesis tests) is that they cannot tell us if relationships between variables are:

important

In a study relating the role of years of education to income for individuals:

in a scatterplot, income is represented on the Y-axis

A regression analysis between sales (Y in $1,000) and advertising (X in $1) resulted in the following equation: Y = 30+4X. The above equation implies that an________.

increase of $1 in advertising is associated with an average increase of $4,000 in sales

Measures of association provide the researcher with information that:

indicates the strength of a relationship between variables

The coefficient of determination:

is the square of the coefficient of correlation

The coefficient of correlation:

is the square root of the coefficient of determination

The intercept of the regression line __________:

is the value of the line where the line crosses the Y-axis

When the null hypothesis in the chi-square test for independence is true, there should be:

little difference between the observed frequencies and the expected frequencies

A least squares regression line:

may be used to predict a value of Y if the corresponding X value is given

The slope of the regression line __________:

means that if X increases by 1 unit, Y increases by

The line described by the regression equation attempts to:

minimize the squared distance from the points

The line of best fit or the regression line:

minimizes the distances between the scatter of points and the regression line

A researcher finds a correlation of .40 between personal income and the number of years of college completed. Based upon this finding he can conclude that:

more years of education are associated with higher income.

If the correlation coefficient is negative, then the coefficient of determination (R2):

must be positive

In linear regression, the correlation coefficient r and the slope coefficient

must have the same sign

What sort of correlation would be expected between a company's expenditure on health and safety and the number of work related accidents.

negative

A researcher reports that her obtained chi-square of -17.56 is significant because it exceeds the critical chi-square of 3.841 for an alpha of .05 with 2 degrees of freedom. What mistake has been made?

neither critical nor calculated chi-square values can have negative values

The table below displays the effects of hair color on political ideology for a sample. How should this relationship be characterized? (Hair Color Blonde Not Blonde Liberal 60% 60% Conservative 40% 40% 100% 100%)

no relationship

For the relationship between social class and movie attendance, a researcher found a gamma of -0.45. This indicates that:

people from higher social classes are less likely to attend movies

Which of the following indicates the strongest relationship?

r = - .6

A chi-square test has been conducted to assess the relationship between marital status and church attendance. The obtained chi-square is 23.45 and the critical chi-square is 9.488. What may be concluded?

reject the null hypothesis, church attendance and marital status are dependent

Which of the following may have an adverse effect on a correlation coefficient?

restricting the range of possible scores

In a bivariate table, the categories of the dependent variable are placed in the:

rows

The p-value for the t-statistic _________:

should be small if the regression model is statistically significant

With reference to the regression equation, β ^ 1 represents the:

slope of the line

The extent to which observed values differ from their predicted values on the regression line is measured by the:

standard error of estimate

A researcher is interested in determining if one could predict the score on a statistics exam from the amount of time spent studying for the exam. In this study, the explanatory variable is:

the amount of time spent studying for the exam

Correlation refers to

the association between two variables

A residual or error is __________:

the difference between an observed value and a predicted value of Y

In a multiple regression problem involving two independent variables, if β ^ 1 is computed to be +2.0, it means that:

the estimated value of Y increases by an average 2 units for each increase of 1 unit of X1, holding X2 constant.

The null hypothesis of regression analysis is __________:

the hypothesized value of the population parameter

When r is negative, one variable increases in value:

the other variable decreases in value

R^2 tells us

the proportion of variability in Y accounted for by X

Given the least squares regression line

the relationship between X and Y is negative

Correlation relates the relative position of a score in one distribution to:

the relative position of a score in another distribution

In a statistics course a linear regression equation was computed to predict the final exam score from the score on the first test. The equation of the least-squares regression line was: Y ^ = 10 + 0.9 X where Y represents the final exam score and X is the score on the first exam. The final exam score is:

the response or dependent variable

If the p-value associated with the regression or slope coefficient is greater than .05, we conclude:

the slope coefficient is not statistically significant, α=.05

The proportion of the variation in the values of Y that is explained by the least squares regression of Y on X is:

the square of the correlation coefficient

Correlation analysis is used to determine

the strength of the relationship between the dependent and the independent variables

Correlation analysis is used to determine:

the strength of the relationship between the dependent and the independent variables

If the F-statistic is statistically significant in a bivariate regression:

the t-statistic for the slope coefficient will be statistically significant

In a research study conducted to determine if arrests were related to the socioeconomic class of the offender, the chi-square critical score was 9.488 and the chi-square test statistic was 12.2. We can conclude that:

the variables are dependent

Unlike other tests of significance, chi-square easily handles situations in which:

the variables of interest have more than two categories or scores

A correlation of -0.5 would indicate a scatterplot where:

there is a moderately good fit between the straight line and the points on the scatterplot

If there is a perfect association between sexual attraction and accelerated heartbeat, then:

there is evidence that sexual attraction and accelerated heartbeat may be causally related

If two variables, X and Y, have are linearly related, then:

there may or may not be any causal relationship between X and Y.

Why is it important to plot a scatterplot before calculating a correlation coefficient for a large dataset.

to ensure the plots are roughly linear

The t-statistic is:

used to test the significance of the individual regression coefficients

To display the effects of the X variable on the Y variable in a bivariate table when the independent variable has been arranged in the columns, compute percentages:

within each column

The value of the chi-square test statistic is always:

zero or a positive number

Data was collected on two variables X and Y and a least squares regression line was fitted to the data. The resulting equation is Y ^ = − 2.29 + 1.7 X . What is the residual for point X=5 and Y=6?

−0.21