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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- The administration of a midwestern university commissioned a salary equity study to help establish benchmarks for faculty salaries. The administration utilized the following regression model for annual salary, y : ?(?) β0+β1x ,where ?=0 if lecturer, 1 if assistant professor, 2 if associate professor, and 3 if full professor. The administration wanted to use the model to compare the mean salaries of professors in the different ranks. a) Explain the flaw in the model. b)Propose an alternative model that will achieve the administration’s objective. c) If the global F-test for the model you proposed in 2 is conducted, what would be the value of the numerator degrees of freedom?arrow_forwardA year-long fitness center study sought to determine if there is a relationship between the amount of muscle mass gained y(kilograms) and the weekly time spent working out under the guidance of a trainer x(minutes). The resulting least-squares regression line for the study is y=2.04 + 0.12x A) predictions using this equation will be fairly good since about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out. B)Predictions using this equation will be faily good since about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent working out C)Predictions using this equation will be fairly poor since only about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out D) Predictions using this equation will be fairly poor since only about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent…arrow_forwardResearchers found a positive assodation between the students' performance in STAT 1000 and their first-year cumulative college GPA. Furthermore, STAT 1000 course GPA explained 62% of the variation in students'first-year cumulative college GPA. The summarized data is given below: Mean STAT 1000 GPA = 25 Std. dev. - 0.21 Mean cumulative College GPA = 325 Std. dev, = 03 The slope and intercept of the least squares regression line for predicting first-year college GPA from STAT 1000 scores are, respectively. Oa Slope 055 Intercept 1.88 Ob Slope = 1.12 Intercept 1.88 Oc Slope = 1.12 Intercept 044 Od. Slope 044 Intercept 055 Oe Slope- 1.88 Intercept 055arrow_forward
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- Suppose 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_forwardThe table below shows the parameters for four multiple linear regression bridge deterioration models. The full model has age as continuous independent variable, traffic (Average Daily Traffic (ADT)) and bridge design as categorical variables. The bridge design is expressed as codes “H’ or “HS” for a single-unit truck and a tractor pulling a semitrailer respectively. The numeric suffix represents the gross weight in tons for H truck or weight on the first two axle sets of the HS truck. For example, H_10 denotes a truck with a gross work of 10 tons. The table also contains the following model validation indicators: adjusted r-squared, Akaike’s Information Criteria (AIC), Mean Absolute Error (MAE) and Bayesian Information Criteria (BIC). Write the multiple regression equation for each of the four models and comment on the accuracy of prediction of bridge deterioration of each model.arrow_forwardThe table below shows the parameters for four multiple linear regression bridge deterioration models. The full model has age as continuous independent variable, traffic (Average Daily Traffic (ADT)) and bridge design as categorical variables. The bridge design is expressed as codes “H’ or “HS” for a single-unit truck and a tractor pulling a semitrailer respectively. The numeric suffix represents the gross weight in tons for H truck or weight on the first two axle sets of the HS truck. For example, H_10 denotes a truck with a gross work of 10 tons. The table also contains the following model validation indicators: adjusted r-squared, Akaike’s Information Criteria (AIC), Mean Absolute Error (MAE) and Bayesian Information Criteria (BIC). Which model is the best predictor model, give logical justification for your answer. Discuss how these models are utilized in Highway Asset management.arrow_forward
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