Concept explainers
The paper “Effects of Canine Parvovirus (CPV) on Gray Wolves in Minnesota” (Journal of Wildlife Management [1995]: 565–570) summarized a regression of y = Percentage of pups in a capture on x = Percentage of CPV prevalence among adults and pups. The equation of the least-squares line, based on n = 10 observations, was
- a. One observation was (25, 70). What is the corresponding residual?
- b. What is the value of the sample
correlation coefficient ? - c. Suppose that SSTo = 2520.0 (this value was not given in the paper). What is the value of se?
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- A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales, in hundreds of thousands of dollars, and profits, in hundreds of thousands of dollars, was investigated by regression. The simple linear regression model displayed was used: profits = a + B (sales), where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation o. This model was fit to the data using the method of least squares. The results displayed were obtained from statistical software. 2 = 0.662 S = 466.2 Parameter Std. err. of Parameter estimate parameter est. -176.644 61.16 0.092498 0.0075 Suppose the researchers test the hypotheses Ho: P = 0, II, : A > 0. The P-value of the test is: less than 0.01. between 0.05 and 0.01. O between 0.10 and 0.05. greater than 0.10. hparrow_forwardSuppose we wish to predict the profits, in hundreds of thousands of dollars, for companies that had sales, in hundreds of thousands of dollars, of 500 units. We use statistical software to do the prediction and obtain the displayed output. St. dev. mean Sales Predict predict 95% C.I. 95% P.I. 500 -130.4 59.3 (-248.5,-12.3) (-1066.4, 805.6) A random sample of 19 companies from the Forbes 500 list was selected, and the relationship between sales, in hundreds of thousands of dollars, and profits, in hundreds of thousands of dollars, was investigated by regression. The simple linear regression model displayed was used: profits a + ß (sales), where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation o. This model was fit to the data using the method of least squares. The results displayed were obtained from statistical software. 2= 0.662 s = 466.2 Parameter Std. err. of estimate parameter est. Parameter -176.644 61.16 0.092498 0.0075 A…arrow_forwardAn article on the cost of housing in California† included the following statement: "In Northern California, people from the San Francisco Bay area pushed into the Central Valley, benefiting from home prices that dropped on average $4,000 for every mile traveled east of the Bay." If this statement is correct, what is the slope of the least-squares regression line, ŷ = a + bx, where y = house price (in dollars) and x = distance east of the Bay (in miles)? Explain. This value is the change in the distance east of the bay, in miles, for each increase of $1 in average home price.This value is the change in the distance east of the bay, in miles, for each decrease of $1 in average home price. This value is the change in the average home price, in dollars, for each increase of 1 mile in the distance east of the bay.This value is the change in the average home price, in dollars, for each decrease of 1 mile in the distance east of the bay.arrow_forward
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