part I The scatterplot below suggests a linear relationship between the age (in
ID: 3290162 • Letter: P
Question
part I
The scatterplot below suggests a linear relationship between the age (in years) of an antique clock and its sale price (in euros) at auction. The data are age and sale price for 11 antique clocks sold at a recent auction. /brainhoney/Resource/5657529,8,0,2,1/Assets/Q25.jpg We fit the least-squares regression line to the model Price = + (Age) where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation . A summary of the output is given: r2 = 0.848 s = 33.1559 Parameter Parameter estimate Std. err. of parameter est. 27.73 34.84 1.893 0.267 Suppose the researchers test the hypotheses H0: = 0, Ha: > 0. The value of the t statistic for this test is
a) –7.090. b) 1.893. c) 7.090. d) 0.796.
part II
The scatterplot below suggests a linear relationship between the age (in years) of an antique clock and its sale price (in euros) at auction. The data are age and sale price for 11 antique clocks sold at a recent auction. /brainhoney/Resource/5657529,8,0,2,1/Assets/Q25.jpg We fit the least-squares regression line to the model Price = + (Age) where the deviations are assumed to be independent and Normally distributed, with mean 0 and standard deviation . A summary of the output is given: r2 = 0.848 s = 33.1559 Parameter Parameter estimate Std. err. of parameter est. 27.73 34.84 1.893 0.267 What percentage of the variation in this data is explained by the age of the clock?
a) 7.8% b) 15.2% c) 84.8% d) 92.2%
Explanation / Answer
H0: = 0, Ha: > 0.
From the output, we get t = 1.893
Option B
r^2 = 0.848 = 84.8%
Option C.
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