Unit 2: Exploring Two-Variable Data

If [math] for a linear regression model, this means:

The least-squares regression line is the line that:

A residual is defined as:

If a residual plot shows a clear curved pattern, this suggests that:

An influential point in regression is a point that:

The regression line [math] predicts that for every one-unit increase in [math]:

Extrapolation in regression is risky because:

A correlation of [math] indicates:

The correlation coefficient between two variables is r = −0.85. Which of the following is the best interpretation?

If the correlation between hours studied and test score is r = 0.80, what proportion of the variation in test scores is explained by hours studied?

A least-squares regression line predicts ŷ = 72 for a given x value. The actual observed value is y = 78. What is the residual?

The regression equation for predicting weight (in pounds) from height (in inches) is ŷ = −150 + 4.5x. Which is the best interpretation of the slope?

A regression model is built using data where x ranges from 10 to 50. Using this model to predict y when x = 80 is called:

A study finds a strong positive correlation between ice cream sales and drowning rates. What is the most likely explanation?

A student scores 2 standard deviations above the mean on a first test. On a retest, the student is most likely to score:

A residual plot shows a clear curved pattern. This suggests that:

Which of the following statements about the correlation coefficient r is TRUE?

If a scatterplot of x vs. y shows an exponential pattern, which transformation might linearize the relationship?

In the regression equation ŷ = 12 + 3x, the y-intercept 12 means:

The standard deviation of the residuals (s) in a regression measures:

Which of the following best describes the relationship shown in the data?

What is the best interpretation of the slope 4.5?

What does the residual plot suggest about the linear model?

What is the best interpretation of r² = 0.81?

What is the equation of the LSRL and is the slope statistically significant?

What effect would removing the point (30, 95) likely have?

What is the predicted weight for a person who is 68 inches tall?

What is the most appropriate conclusion from this study?

A least-squares regression equation is ŷ = 2.3 + 0.45x, where x is hours studied and y is exam score. The coefficient of determination is r² = 0.64. Which of the following is the best interpretation?

A scatterplot of log(y) versus x shows a roughly linear pattern with equation log(ŷ) = 1.2 + 0.08x. What is the predicted value of y when x = 10?

A least-squares regression equation is ŷ = 2.4 + 0.8x with r² = 0.64. A data point has x = 10 and y = 14. What is the residual for this point?

A scatterplot shows a strong curved relationship between x and y. After applying a log transformation to y, the resulting scatterplot of x vs log(y) appears linear with r = 0.97. Which conclusion is most appropriate?