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Which one of the following provides evidence that a condition for regression inference has been met?
A Normal probability plot of the values for the explanatory variable shows a roughly linear form.
A scatterplot of the residuals against the values of the explanatory variable displays a random scattering of points about the line residuals = 0.
The data consists of at least 30 observations.
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. Which one of the following is a correct set of hypotheses for testing the significance of this relationship?
H0 : β = 1, Ha: β ≠ 1, where β = the true slope of the population regression line.
H0 : β = 0, Ha: β ≠ 0, where β = the true slope of the population regression line.
H0 : ρ = 1, Ha: ρ < 1, where ρ = the true population correlation between age and reaction time.
H0 : ρ = 0, Ha: ρ < 0, where ρ = the true population correlation 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 below. The equation of the least-squares regression line is
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.
Sarah runs an ice cream stand at a beach resort, and she is interested in predicting each day’s ice cream sales (in dollars) from the air temperature at 8:00 am (in degrees Fahrenheit). She randomly selects 12 days during the previous summer and calculates a least squares regression of sales on air temperature. A computer output of her regression is given below. Which one of the following is a correct interpretation of the number 1.646?
For each 1° increase in air temperature, ice cream sales are predicted to increase, on average, by $1.65
For samples of size 12, the typical deviation of a sample slope from the population (true) slope is estimated to be 1.646
For this sample, the typical distance between an observed temperature and the mean temperature is 1.646
Forestry managers keep records giving the number of board feet B (in hundreds of board feet) of lumber produced by harvesting white pine trees with diameter D (in inches), so that they can predict the amount of lumber that can be harvested from a tree from its diameter. A scatterplot of B vs. D shows a strongly curved shape, but taking the natural logarithm of both variables produces a linear scatterplot. This computer output below is for a least squares linear regression of vs for 9 white pine trees. Which one of the following is a correct regression equation for these data?
With practice, people become faster at solving a certain type of mathematical puzzle. Fourteen college students were allowed to practice completing a certain type of mathematical puzzle for different amounts of time. Afterwards, each student’s completion time on a new puzzle was measured. The Residual plot for regression of Completion Time on Practice Time is shown below. Which of the following is correct?
There is a no relationship between Practice Time and Puzzle Completion Time.
This regression equation would likely overestimate the Puzzle Completion Time for 175 minutes of practice time.
There is a non-linear relationship between Practice Time and Puzzle Completion Time.
What is the regression estimated regression equation
expected sale price = 16.470 -0.059 mileage
expected mileage = 16.470 -0.059 sale price
y = 16.470 - 0.059 x
x = 16.470 - 0.059 y
What is the the result of the test Ho: b1 = 0 H1 : b1 ≠ 0 at the significance level of 5%?
Reject the null hypothesis, because the p value i=0 is less than the significance level.
Accept the null hypothesis, because the p value i=0 is less than the significance level.
Accept the null hypothesis, because the t-stat = 17.359 is larger than 2.
There is not enough information.
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