Suppose a logistic model has been fitted to a data set and the ROC curve has been plotted. If the point with sensitivity = a and specificity = B is on the curve, what are the smallest and largest values for the area under the curve?
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![Suppose a logistic model has been fitted to a data set and the ROC curve has been plotted. If the
point with sensitivity = a and specificity = B is on the curve, what are the smallest and largest values
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- A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter2) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper. BMI Change (kg/m²) Depression Score Change S = The accompanying computer output is from Minitab. Depression score change 15- 10- -0.5 S Fitted Line Plot Depression score change = 6.577 +5.440 BMI change 20- 5.30586 Coefficients T 0.0 0.5 -0.5 R-sq 25.96% - 1 Term Coef Constant 6.577 BMI change 5.440 % 0.5 BMI change 1.0 SE Coef 2.28 2.90 9 0 0.1 0.7 0.8 1 1.5 4 T-Value 2.88 1.87 Interpret this estimate. s is the typical amount by which the ---Select--- line. 4 5 Regression Equation Depression score change = 6.577 +5.440 BMI change P-Value 0.0164 0.0906 S 5.30586 25.96% R-Sq R-Sq (adj) 18.56% 8 (b) Give a point estimate of o. (Round your answer to…The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. The table contains data for beak heat loss, as a percentage of total body heat loss from all sources, at various temperatures in degrees Celsius. The data show that beak heat loss is higher at higher temperatures and that the relationship is roughly linear. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (oC)(oC) Percent heat loss from beak 1515 3434 1616 3535 1717 3333 1818 3333 1919 3535 2020 4848 2121 5454 2222 5252 2323 4545 2424 5050 2525 4444 2626 5454 2727 5959 2828 6262 2929 6464 3030 6161 Adapted from a graph in…A researcher is interested in testing the relationship between smoking and BMI (kg/m2) in adults aged 30-45. In order to test this association, the researcher divides smoking into currently more than a pack a day, currently less than a pack a day, and never smokers. The following table represents the BMIs for each participant enrolled by their respective smoking category. Current Smoker (≥1pack/day) Current Smoker (<1 pack/day Never Smoked 26.7 29.4 22.1 29.4 28.6 30.4 24.3 27.4 21.3 28.4 23.2 26.4 21.6 20.1 19.7 27.4 20.6 19.8 26.8 19.7 21.6 36.4 19.6 22.3 31.5 21.6 24.3 27.4 21.5 *Continue as though all assumptions for ANOVA are met. A) Calculate the MSW and MSB for the data represented above. B) Carry out a formal test for a one-way analysis of variance among the groups and interpret your results.
- Reliability testing of the new 2.0 liter Chevy automotive engine has resulted in a time to failure distribution which is lognormal with = 90,000 mi. and s = 0.60. Find: med %3D a. R(40,000 mi.) b. MTTF and Std. Dev. c. R(90,000|40,000) d. t .90Water is poured into a large, cone-shaped cistern. The volume of water, measured in cm, is reported at Which of the following would linearize the data for volume and time? different time intervals, measured in seconds. The scatterplot of volume versus time showed a curved Seconds, cm3 O In(Seconds), cm3 Seconds, In(cm') pattern. O In(Seconds), In(cm³)Suppose that a customer is purchasing a car. He conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. He conducts this experiment 15 times on each car and records the number of miles driven. Median for Car 2 M = 250 mi / 10 gal (Type an integer or decimal rounded to one decimal place as needed.) Full data setO Range for Car 1 R=O mi / 10 gal (Type an integer or decimal rounded to one decimal place as needed.) Car 1 245 242 215 244 220 265 291 160 284 251 169 319 257 306 267 Range for Car 2 R=O mi / 10 gal (Type an integer or decimal rounded to one decimal place as needed.) Car 2 230 206 214 236 242 256 245 255 241 264 276 252 250 251 257
- Shortleaf Pines. The ability to estimate the volume of a tree based on a simple measurement, such as the diameter of the tree, is important to the lumber industry, ecologists, and conservationists. Data on volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines was reported in C. Bruce and F. X. Schumacher’s Forest Mensuration (New York: McGraw-Hill, 1935) and analyzed by A. C. Akinson in the article “Transforming Both Sides of a Tree” (The American Statistician, Vol. 48, pp. 307–312). The data are provided on the WeissStats site. a. obtain and interpret the standard error of the estimate. b. obtain a residual plot and a normal probability plot of the residuals. c. decide whether you can reasonably consider Assumptions 1–3 for regression inferences met by the two variables under consideration.You want to conduct a study on the proportion of Penn State students who miss class when it is raining. Suppose here is the data you collect for students who live on-campus versus students who live off-campus: Never Miss Sometimes Miss Always Miss On-Campus 20 12 13 Off-Campus 45 14 22 a. For on-campus students (only), estimate the true difference in proportions for those who never miss class versus those who always miss class, when it is raining. Place a bound on the error of estimation. b. Estimate the true difference between the proportions of on-campus students who always miss class versus the proportion of off-campus students who always miss class, when it is raining. Place a bound on the error of estimation.Some people don't gain weight even when they overeat. Perhaps fidgeting and other “nonexercise activity" (NEA) explains why – the body might spontaneously increase nonexercise activity when fed more. Researchers deliberately overfed 16 healthy young adults for 8 weeks. They measured fat gain (y, in kilograms) and increase in energy use (NEA) (x, in calories), as an explanatory variable, from activity other than deliberated exercise – fidgeting, daily living, and the like. Here are the data (sorted by NEA): NEA increase -94 -57 -29 135 143 151 245 355 620 690 Fat gain 4.2 3.0 3.7 2.7 3.2 3.6 2.4 1.3 2.3 1.1 Assume that the model Fat gain= Bo +B,NEA increase +ɛ is reasonable. Selected SAS output are given here. 0.73985 R-Square 0.6061 2.38750 Adj R-Sq 0.5780 Root MSE Dependent Mean Coeff Var 30.98860 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > It| Intercept 1 3.50512 0.30362 11.54 <.0001 1 -0.00344 0.00074141 -4.64 0.0004 nea (a) Find the average fat…
- The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Presented is the data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.] Temperature (°C) 1515 1616 1717 1818 1919 2020 2121 2222 2323 2424 2525 2626 2727 2828 2929 3030 Percent heat loss from beak 3232 3636 3636 3333 3535 4747 5757 5151 4242 5353 4646 5252 5959 5959 6363 6262 (a) What is the equation of the least‑squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature? (Use…A researcher collects data that represents the average number of hours of sleep in the last two nights by 8 depressed patients and 9 non-depressed patients. The researcher is interested in whether the two groups reliably differ in the amount of sleep they get. Use Jamovi to calculate t-obt and the p value.Seedlings of understory trees in mature tropical rainforests must survive and grow using intermittent flecks of sunlight. How does the length of exposure to these flecks of sunlight (fleck duration) affect growth? Researchers experimentally irradiated seedlings of the Southeast Asian rainforest tree with flecks of light of varying duration while maintaining the same total irradiance to all the seedlings. Below is the data. Fit a linear model to the data. Tree Mean Fleck (min) Relative growth rate (mm/mm/week 1 3.4 0.013 2 3.2 0.008 3 3 0.007 4 2.7 0.005 5 2.8 0.003 6 3.2 0.003 7 2.2 0.005 8 2.2 0.003 9 2.4 0 10 4.4 0.009 11 5.1 0.01 12 6.3 0.009 13 7.3 0.009 14 6 0.016 15 5.9 0.025 16 7.1 0.021 17 8.8 0.024 18 7.4 0.019 19 7.5 0.016 20 7.5 0.014 21 7.9 0.014 a)What is the rate of change in relative growth…
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