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Solved: Diamonds sold at retail. Refer to the Journal of
Chapter 11, Problem 101SE(choose chapter or problem)
Diamonds sold at retail. Refer to the Journal of Statistics Education study of 308 diamonds sold on the open market, Exercise 2.158 (p. 117). Recall that you related the size of the diamond (number of carats) to the asking price (dollars) using a scatterplot.
a. Write the equation of a straight-line model relating asking price (y) to number of carats (x).
b. An XLSTAT simple linear regression printout for the analysis is shown on the following page. Find the equation of the least squares line.
c. Give a practical interpretation of the y-intercept of the least squares line. If a practical interpretation is not possible, explain why.
d. Locate a 95% confidence interval for the slope of the least squares line on the printout and practically interpret the result. Over what range is the interpretation meaningful?
e. Locate the estimated standard deviation of the random error on the printout and practically interpret this value.
f. Specify the null and alternative hypotheses for determining whether a positive linear relationship exists between asking price and size.
g. Locate the p-value of the test, part f, on the printout. Interpret the result if \(\alpha\ =\ .05\).
h. Locate the coefficient of determination, \(r^2\) , on the printout and interpret the result.
i. Locate the coefficient of correlation, r, on the printout and interpret the result.
j. Locate a 95% prediction interval for the asking price when carat size is .5 on the printout and practically interpret the result.
k. Locate a 95% confidence interval for the mean asking price when carat size is .5 on the printout and practically interpret the result.
Questions & Answers
QUESTION:
Diamonds sold at retail. Refer to the Journal of Statistics Education study of 308 diamonds sold on the open market, Exercise 2.158 (p. 117). Recall that you related the size of the diamond (number of carats) to the asking price (dollars) using a scatterplot.
a. Write the equation of a straight-line model relating asking price (y) to number of carats (x).
b. An XLSTAT simple linear regression printout for the analysis is shown on the following page. Find the equation of the least squares line.
c. Give a practical interpretation of the y-intercept of the least squares line. If a practical interpretation is not possible, explain why.
d. Locate a 95% confidence interval for the slope of the least squares line on the printout and practically interpret the result. Over what range is the interpretation meaningful?
e. Locate the estimated standard deviation of the random error on the printout and practically interpret this value.
f. Specify the null and alternative hypotheses for determining whether a positive linear relationship exists between asking price and size.
g. Locate the p-value of the test, part f, on the printout. Interpret the result if \(\alpha\ =\ .05\).
h. Locate the coefficient of determination, \(r^2\) , on the printout and interpret the result.
i. Locate the coefficient of correlation, r, on the printout and interpret the result.
j. Locate a 95% prediction interval for the asking price when carat size is .5 on the printout and practically interpret the result.
k. Locate a 95% confidence interval for the mean asking price when carat size is .5 on the printout and practically interpret the result.
ANSWER:Step 1 of 11
a)
The equation of a straight line model is given below:
Where, y denotes the response variable (asking price).
x denotes the predictor variable (number of carats).
