In the equation y = a + bx, the value a is the y-intercept, the value of y when x is 0.
Correct Answer
True
True. Setting x = 0 in y = a + bx leaves y = a, so a is where the line crosses the y-axis. The value b is the slope.
Category: Linear Equations
Question 2
A line with a negative slope rises from left to right.
Correct Answer
False
False. A line with a negative slope falls from left to right, because y decreases as x increases. A line with a positive slope rises, and a slope of 0 gives a horizontal line.
Category: Linear Equations
Question 3
A scatter plot is used to display the relationship between two quantitative variables.
Correct Answer
True
True. Each point on a scatter plot shows one pair of values (x, y). The overall pattern reveals the direction, form and strength of the relationship.
Category: Scatter Plots
Question 4
A correlation coefficient of -0.9 indicates a weaker linear relationship than a correlation coefficient of 0.5.
Correct Answer
False
False. Strength depends on the absolute value of r, and |-0.9| = 0.9 is larger than 0.5, so -0.9 shows the stronger relationship. The negative sign only indicates that y tends to decrease as x increases.
Category: Correlation
Question 5
The sign of the correlation coefficient always matches the sign of the slope of the least-squares line.
Correct Answer
True
True. The slope is b = r(sy / sx), and standard deviations are positive, so b and r always have the same sign. A positive r gives an upward line and a negative r gives a downward line.
Category: Least-Squares Line
Question 6
If r = 0.7, then 70% of the variation in y is explained by the regression line.
Correct Answer
False
False. The share explained is r^2, not r. With r = 0.7, r^2 = 0.49, so 49% of the variation in y is explained by the line and 51% is not.
Category: Correlation
Question 7
The least-squares regression line always passes through the point (x-bar, y-bar).
Correct Answer
True
True. Because the intercept is a = y-bar - b(x-bar), substituting x = x-bar into the line gives y-hat = y-bar. The point of means is always on the line.
Category: Least-Squares Line
Question 8
A residual is calculated as the predicted value minus the observed value.
Correct Answer
False
False. A residual is the observed value minus the predicted value, y - y-hat. With this definition, a point above the line has a positive residual.
Category: Least-Squares Line
Question 9
A positive residual means the observed point lies above the regression line.
Correct Answer
True
True. A positive residual means y is larger than y-hat, so the point sits above the line and the line underestimates y there. A negative residual means the point is below the line.
Category: Least-Squares Line
Question 10
A strong correlation between two variables proves that one variable causes the other.
Correct Answer
False
False. Correlation does not imply causation. A strong association can come from a lurking variable or from coincidence, and only a well-designed experiment can support a causal claim.
Category: Correlation
Question 11
One assumption of the significance test for the correlation coefficient is that, for each x, the y values are normally distributed about the regression line.
Correct Answer
True
True. The test assumes a linear relationship, y values normally distributed about the line at each x, equal spread of those y values for every x, independent residuals, and data from a random sample or randomized experiment.
Category: Significance Testing
Question 12
When a test finds that the population correlation is not significantly different from zero, the regression line should still be used to make predictions.
Correct Answer
False
False. If the correlation is not significant, the data do not show a linear relationship, so the line should not be used for prediction. The line is used for prediction only when the correlation is significant.
Category: Significance Testing
Question 13
A residual plot with no visible pattern supports the use of a linear model.
Correct Answer
True
True. When residuals scatter randomly around zero with a roughly constant spread, a straight line is a reasonable model. A curve or a funnel shape in the residual plot suggests the linear model is a poor fit.
Category: Outliers
Question 14
The slope of the least-squares line is found by multiplying r by sx / sy.
Correct Answer
False
False. The slope is b = r(sy / sx), with the standard deviation of y on top. The slope is measured in units of y per unit of x, which this ratio provides.
Category: Least-Squares Line
Question 15
If every data point lies exactly on a straight line with a positive slope, the correlation coefficient equals 1.
Correct Answer
True
True. A correlation of 1 means a perfect positive linear relationship, with every point on an upward line. A correlation of -1 means every point lies on a downward line.
Category: Correlation
Question 16
The correlation coefficient changes when the x values are converted from inches to centimeters.
Correct Answer
False
False. The correlation coefficient has no units, so changing the units of either variable leaves r unchanged. Converting units only stretches the scale of the scatter plot without changing the pattern.
Category: Correlation
Question 17
An outlier in regression is a point that lies far from the least-squares line, giving it a large residual.
Correct Answer
True
True. Outliers are observed points far from the line in the vertical direction, so their residuals are unusually large in absolute value. A common check flags residuals of at least two standard deviations of the residuals.
Category: Outliers
Question 18
The standard deviation of the residuals, s, is found by dividing SSE by n - 1 and then taking the square root.
Correct Answer
False
False. The standard deviation of the residuals is s = sqrt(SSE / (n - 2)). Two degrees of freedom are used up by estimating the slope and the intercept.
Category: Outliers
Question 19
An outlier should be examined before deciding whether to remove it, because it may be a data error or may carry real information.
Correct Answer
True
True. An outlier can come from a recording mistake, which should be corrected, or it can be a genuine and informative value. If a point is removed, the researcher should report that and explain why.
Category: Outliers
Question 20
The value of r^2 can be negative when the relationship between x and y is negative.
Correct Answer
False
False. Squaring any number gives a result that is zero or positive, so r^2 is always between 0 and 1. The direction of the relationship shows up only in the sign of r.
Category: Correlation