Question 1

If the slope (b)is zero,the value of r

Accepted Answer

When the slope (b) is zero, it means there is no linear relationship between the two variables. Therefore, the correlation coefficient (r) would also be zero.

Question 2

The explained variation represents

Accepted Answer

The explained variation, also known as the variation accounted for, represents the improvement in our ability to predict Y when taking X into account. It is measured by the difference between the total variation and the residual variation, and is an important measure of the strength of the relationship between X and Y in a regression model.

Question 3

If a = 5 and b = 10,what would the value of Y be when X = 100?

Accepted Answer

There is no direct relation given between a, b, and x, therefore we can ignore them. We only have to find the value of y when x is 100. Therefore, the answer is independent of a and b. So the value of y will be equal to 1005 because it's already given. Therefore, the correct answer is C.

Question 4

If a = 2 and b = 4,what would the value of Y be when X = 1?

Accepted Answer

The answer of If a = 2 and b =...

Question 5

If the regression line showing the effect of education on income has a slope of 1000,

Accepted Answer

A slope of 1000 means that for every increase in education by 1 year, income increases by 1000. Therefore, every year of education increases income by 1000.

Question 6

The coefficient of determination may be interpreted with a logic akin to

Accepted Answer

The coefficient of determination, also known as R-squared, is a measure of how well the regression line fits the data. It represents the proportion of the variance in the dependent variable that is explained by the independent variable(s). PRE (Proportional Reduction in Error) is another term for the coefficient of determination and is often used interchangeably. Therefore, option C is the best choice as it correctly relates to the interpretation of the coefficient of determination.

Question 7

One important function of the least-squares regression equation is that

Accepted Answer

The least-squares regression equation allows us to predict Y scores for any value of X. It does not tell us if a relationship is linear or make the scattergram symmetrical, and it does not summarize all possible scores on the two variables.

Question 8

The amount of error in predicting Y that remains after X has been taken into account is

Accepted Answer

The amount of error in predicting Y that remains after X has been taken into account is referred to as the unexplained variation of Y or the residual variation of Y. This represents the variability in Y that cannot be explained by the linear relationship with X. Therefore, only option A is correct.

Question 9

When working with interval-ratio data,the optimal strategy for predicting Y while ignoring X will be to use the

Accepted Answer

When working with interval-ratio data, the most appropriate strategy for predicting Y while ignoring X is to use the mean Y score for every case. The mean is the best measure of central tendency when dealing with interval-ratio data since it takes all data points into account and is the most representative of the overall data. The mode and median are not as appropriate for interval-ratio data since they do not consider all data points and may not be representative of the entire dataset. Using the lowest Y score for every case would be an incorrect strategy since it could lead to inaccurate predictions and does not take into account the distribution of the data.

Question 10

The position of the least-squares regression line is defined by two elements:

Accepted Answer

The Y intercept and the slope of the line determine the position of the least-squares regression line. The Y intercept is the point where the line intersects the Y axis, and the slope determines the steepness and direction of the line. The X intercept and the intersection point of the X and Y axes are not relevant in determining the position of the least-squares regression line.

Question 11

If a regression line is parallel to the horizontal axis of the scattergram,the slope (b)will be

Accepted Answer

If the regression line is parallel to the horizontal axis, it means that there is no relationship between the independent and dependent variables, and hence the slope (b) will be 0.00.

Question 12

If the slope of a regression line is 1.5,then

Accepted Answer

The slope of a regression line represents the change in Y for every unit of change in X. Therefore, if the slope is 1.5, for every unit of change in X, there is a change of 1.5 units in Y.

Question 13

When working with interval-ratio data,the optimal strategy for predicting Y while taking X into account would be to

Accepted Answer

When working with interval-ratio data, the best strategy for predicting Y while taking X into account would be to use the regression line. The regression line is calculated using the slope (b) and the Y intercept (a), so ignoring the slope or always predicting the Y intercept would not be an optimal strategy. Guessing randomly also would not provide any useful predictions. Therefore, the best choice is to use the regression line.

Question 14

The slope (b)is an awkward measure of the strength of a relationship because

Accepted Answer

The slope can be any real number, not limited to 1.00, and its magnitude depends on the units of the variables, not the strength of the relationship.

Question 15

A study of traffic safety show a correlation of 0.57 between average speed of traffic and number of fatal accidents for a particular stretch of highway.This means that

Accepted Answer

The correlation coefficient of 0.57 suggests a moderate positive correlation between average speed and number of fatal accidents. This means that as average speed increases, we can expect fatalities to increase as well. However, it does not necessarily mean that speed is the sole cause of the fatalities, as there may be other factors (such as road conditions or driver behavior) that also contribute to these accidents. Therefore, choice C – "fatalities tend to increase as average speed increases" – is the most appropriate answer.

Question 16

A researcher wants to measure the strength of the association between income (measured in dollars per year)and education (measured in number of years of formal schooling).Which of the following would be the most appropriate measure of association?

Accepted Answer

Pearson's r is the most appropriate measure of association for measuring the strength of the linear relationship between two continuous variables, such as income and education. The slope (b) would only measure the strength of the linear relationship between income and education in a regression model, whereas gamma and chi square are typically used for measuring the strength of association between two categorical variables.

Question 17

A researcher asked a sample of dual career families about the percentage of the family budget contributed by the wife's job (Y)and the total number of children (X).Pearson's r for this relationship is -0.34.Which of the following is an appropriate interpretation of these results?

Accepted Answer

Pearson's r of -0.34 indicates a negative correlation between X (number of children) and Y (percentage of family budget contributed by the wife). Therefore, as the number of children increases, the percentage of the budget contributed by the wife decreases. Option D correctly interprets this relationship. Option A is incorrect as the correlation coefficient cannot be interpreted in terms of causal relationships. Option B is not supported by the given data. Option C is too extreme and not supported by the data.

Question 18

The Y intercept is the point where

Accepted Answer

The Y intercept, or the point where the regression line crosses the vertical axis of the scattergram, represents the predicted value of Y when X equals zero.

Question 19

If you wanted to measure the association between the age of people (in years)and the number of arrests for driving while intoxicated,the most appropriate measure of association would be

Accepted Answer

Pearson's r is the most appropriate measure of association for continuous variable data, such as age and number of arrests. Gamma and lambda are measures of association for ordinal data, while phi is a measure of association for nominal data.

Question 20

In regression analysis,the symbol a stands for

Accepted Answer

In regression analysis, a stands for the Y intercept. It is the point at which the regression line crosses the Y-axis.

Quiz 15: Association Between Variables Measured at the Interval-Ratio Level

If the slope (b) is zero,the value of r