AP Statistics Inference for Regression

What's the appropriate interpretation of the slope of the regression line?

• For every additional 0.61 hours of growth, the culture is predicted to weight 1 more gram.

• For every additional hour of growth, the culture is predicted to weigh 0.61 more grams.

• For every additional hour of growth, the logarithm of the culture's weight in grams is predicted to increase by 0.61.

• At the beginning of the experiment, the logarithm of the culture's weight in grams was approximately 0.61 ounces.

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. We collected data on the appraised market values x and the actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data. The equation of the least-squares regression line for predicting selling price from appraised value is

Describe the correlation in the graph shown.

• Strong Negative

• Strong Positive

• Weak Negative

• Weak Positive

Describe the correlation in the graph shown.

• Strong Negative

• Strong Positive

• Weak Negative

• Weak Positive

Which of the following is the regression equation for this data?

• Price^ = 87.3180 - 19.4(Area)

• Price^ = -19.4 + 0.1297(Area)

• Area^ = -19.4 + 0.1297(Price)

• Price^ = 0.1297 - 19.4(Area)

Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given. Which of the following is the correct decision for the test of H0 : β = 0 versus Ha : β ≠ 0 at the α = 0.05 level? Assume all conditions for inference have been met.

• Because the P-value is less than the significance level, we reject H₀. There is strong evidence of a linear relationship between age and reaction time.

• Because the P-value is 0.365, which is more than a 5% significance level, we fail to reject H₀. We do not have evidence of a linear relationship between age and reaction time.

• Because the P-value is less than the significance level, we fail to reject H₀. We do not have evidence of a linear relationship between age and reaction time.

• Because the P-value is 0.365, which is more than a 5% significance level, we reject H₀. There is strong evidence of a linear relationship between age and reaction time.

Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given. Which of the following is the correct decision for the test of H0 : β = 0 versus Ha : β ≠ 0 at the α = 0.05 level? Assume all conditions for inference have been met.

• Because the P-value is less than the significance level, we reject H0. There is strong evidence of a linear relationship between age and reaction time.

• Because the P-value is 0.365, which is more than a 5% significance level, we fail to reject H0. We do not have evidence of a linear relationship between age and reaction time.

• Because the P-value is less than the significance level, we fail to reject H0. We do not have evidence of a linear relationship between age and reaction time.

• Because the P-value is 0.365, which is more than a 5% significance level, we reject H0. There is strong evidence of a linear relationship between age and reaction time.

Which of the following statements about the slope of the least-squares regression line is true? 

• It has the same sign as the correlation coefficient r.

• The square of the slope equals the proportion of the variation in the response variable that is explained by the explanatory variable.

• It is unitless.

• When the x-variable is 0, this is what the y-variable is predicted to be.

Is there a relationship between reaction time and age? A statistics student measures the reaction time of 12 subjects by measuring how far a yardstick drops, in inches, before a subject catches it between his or her thumb and forefinger (a high number thus indicates a slow reaction time). The student plans to use linear regression to see if reaction time can be predicted by the age of the subject. Output from a computer regression analysis is given below. The equation of the least-squares regression line is

• 
• 
• 

In a regression line of Yon X the variable Xis known as

• independent variables

• regressior

• explanatory variable

• all of the above