BIOS 3000 Quiz 4

Before surgical removal of a diseased parathyroid gland, two tests are often performed: the standard intact test and the turbo test. Both tests measure parathyroid hormone (PTH, in ng/l), but the turbo test is very expensive. Researchers obtained data from both tests in a sample of 48 patients to predict turbo test results (y) from standard intact test results (x). The data ranged from roughly 0 to 500 ng/l, and a scatterplot showed a clear linear relationship. The published findings are summarized exactly as follows: y=−4.36+1.08x (r=0.97, n=48) What is the slope of the regression line?

1.08

efore surgical removal of a diseased parathyroid gland, two tests are often performed: the standard intact test and the turbo test. Both tests measure parathyroid hormone (PTH, in ng/l), but the turbo test is very expensive. Researchers obtained data from both tests in a sample of 48 patients to predict turbo test results (y) from standard intact test results (x). The data ranged from roughly 0 to 500 ng/l, and a scatterplot showed a clear linear relationship. The published findings are summarized exactly as follows: y=−4.36+1.08x (r=0.97, n=48) For a PTH level of X=100 ng/l with the standard intact test, what is the predicted PTH level with the turbo test?

103.64 ng/l

Data on the water quality in the eastern United States were obtained by a researcher who wanted to ascertain whether the amount of particulates in water (ppm) could be used to accurately predict the water quality score. A simple linear regression model was fit to the data using the method of least squares. The following results were obtained from statistical software based on a sample of size 61: R2=0.005, sy|x=0.7896 Which of the following is the correct interpretation of the estimated slope βˆ1 of the regression line?

It is estimated that water quality score decreases by 0.009 units, on average, for every 1 ppm increase in the amount of particulates in the water.

A fisheries biologist has been studying horseshoe crabs. She has sampled 173 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). A simple linear regression model was fit to the data with width as the explanatory variable and weight as the response variable using the method of least squares. The following results were obtained from R: What is the 95% confidence interval for the slope β1 in the simple linear regression model?

(0.224, 0.262)

Suppose we are interested in predicting the weight of a horseshoe crab with width 22.5 centimeters. Using R, we generated two different interval estimates (shown in the table below: Which of the intervals in the table is the 95% interval for the mean weight of horseshoe crabs with width 2.25 centimeters?

(1.43, 1.60)

A fisheries biologist has been studying horseshoe crabs. She has sampled 173 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). A simple linear regression model was fit to the data with width as the explanatory variable and weight as the response variable using the method of least squares. The following results were obtained from R: Based on the sample data, what is the correlation between the width and weight of horseshoe crabs?

0.8868

A fisheries biologist has been studying horseshoe crabs. She has sampled 173 horseshoe crabs and recorded their weight (in kilograms) and width (in centimeters). A simple linear regression model was fit to the data with width as the explanatory variable and weight as the response variable using the method of least squares. The following results were obtained from R: Suppose the researchers test the following hypotheses:H0:β1=0, HA:β1≠0 What is the value of the t statistic for this test?

25.1

Before surgical removal of a diseased parathyroid gland, two tests are often performed: the standard intact test and the turbo test. Both tests measure parathyroid hormone (PTH, in ng/l), but the turbo test is very expensive. Researchers obtained data from both tests in a sample of 48 patients to predict turbo test results (y) from standard intact test results (x). The data ranged from roughly 0 to 500 ng/l, and a scatterplot showed a clear linear relationship. The published findings are summarized exactly as follows: y=−4.36+1.08x (r=0.97, n=48) Roughly what percent of the variation in turbo test results can be explained by this regression model?

94%

Before surgical removal of a diseased parathyroid gland, two tests are often performed: the standard intact test and the turbo test. Both tests measure parathyroid hormone (PTH, in ng/l), but the turbo test is very expensive. Researchers obtained data from both tests in a sample of 48 patients to predict turbo test results (y) from standard intact test results (x). The data ranged from roughly 0 to 500 ng/l, and a scatterplot showed a clear linear relationship. The published findings are summarized exactly as follows: y=−4.36+1.08x (r=0.97, n=48) For a PTH level of X=1000 ng/l with the standard intact test, what is the predicted PTH level with the turbo test?

Cannot be predicted accurately because it would be extrapolation

Data on the water quality in the eastern United States were obtained by a researcher who wanted to ascertain whether the amount of particulates in water (ppm) could be used to accurately predict the water quality score. A simple linear regression model was fit to the data using the method of least squares. The following results were obtained from statistical software based on a sample of size 61: R2=0.005, sy|x=0.7896 Which of the following is the correct interpretation of the estimated intercept βˆ0 of this regression line?

The average water quality score is estimated to be 6.214 when there are no particulates in the water (0 ppm).