In a study to predict temperature from air pressure in a piston-cylinder device, 19measurements were made of temperature in °F (y) and air pressure in psi (x). Three modelswere fit: the linear model y = Bo + B,x + ɛ, the quadratic model y = Bo + Bix + B2x² + ɛ, andthe cubic model y = Bo + B,x + B2x? + Bx3 + E. The residuals and fitted values for eachmodel are presented in the following table. Plot the residuals versus the fitted values foreach model. For each model, state whether the model is appropriate, and explain.%3DQuadratic ModelFitLinear ModelCubic ModelResidualFitResidualResidualFit-56.2125.611.258.23.366.1-34.0153.1-7.4126.5-6.7125.78.4179.84.9183.49.2179.021.4207.2-3.6232.20.9227.828.6234.7-8.2271.5-5.9269.246.9260.98.1299.77.3300.547.2288.115.7319.612.1323.28.5314.4-7.0329.8-11.7334.6-7.1342.04.0330.91.0333.9-47.1139.3-1.393.6-4.196.4-1.6166.29.1155.512.1152.538.0220.95.9253.09.5249.4247.8286.7286.0313.735.7-3.2-2.434.1275.1-2.1311.3-4.534.6301.19.9325.85.5330.21.0328.2-2.4331.6-6.7335.9-23.2355.34.1327.93.5328.5-50.7368.4-5.0322.7-2.1319.9-72.9382.1-5.7314.92.1307.1

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Answered: In a study to predict temperature from…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A company that manufactures computer chips wants to use a multiple regression model to study the effect that 3 different variables have on y, the total daily production cost (in thousands of dollars). Let B,, B,, and B, denote the coefficients of the 3 variables in this model. Using 22 observations on each of the variables, the software program used to find the estimated regression model reports that the total sum of squares (SST) is 485.84 and the regression sum of squares (SSR) is 229.91. Using a significance level of 0.10, can you conclude that at least one of the independent variables in the model provides useful (i.e., statistically significant) information for predicting daily production costs? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (a) State the null hypothesis H, for the test. Note that the alternative hypothesis H, is given. H, :0 H, : at least one of the independent variables is useful…
An airline developed a regression model to predict revenue from flights that connect "feeder" cities to its hub airport. The response in the model is the revenue generated by flights operating to the feeder cities (in thousands of dollars per month), and the two explanatory variables are the air distance between the hub and feeder city (Distance, in miles) and the population of the feeder city (in thousands). The least squares regression equation based on data for 37 feeder locations last month is Estimated revenue = 81 +0.3Distance + 1.4Population with R² = 0.75 and so = 31.2. Complete parts a through d. (a) The airline plans to expand its operations to add an additional feeder city. The first possible city has population 150,000 and is 275 miles from the hub. A second possible city has population 180,000 and is 250 miles from the hub. Which would you recommend if the airline wants to increase total revenue? The first city The second city
The authors of a paper investigated whether water temperature was related to how far a salamander would swim and whether it would swim upstream or downstream. Data for 14 streams with different mean water temperatures where salamander larvae were released are given (approximated from a graph that appeared in the paper). The two variables of interest are x = mean water temperature (°C) and y = net directionality, which was defined as the difference in the relative frequency of the released salamander larvae moving upstream and the relative frequency of released salamander larvae moving downstream. A positive value of net directionality means a higher proportion were moving upstream than downstream. A negative value of net directionality means a higher proportion were moving downstream than upstream. Mean Temperature (x) Net Directionality (y) 6.22 −0.08 8.01 0.25 8.67 −0.14 10.61 0.00 12.5 0.08 11.94 0.03 12.55 −0.07 17.93 0.29 18.34 0.23…
The following table shows the length, in centimeters, of the humerus and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles. (A graphing calculator is recommended.) (a) Find the equation of the least-squares regression line for the data. (Where × is the independent variable.) Round constants to the nearest hundredth. y= ? (b) Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 52 centimeters. ? cm
A study examined the eating habits of 20 children at a nursery school. The variables measured for each child included: calories (the number of calories eaten at lunch), time (the time in minutes spent eating lunch), and sex (male=1, female=0). A multiple linear regression model using Y = calories, X1 = time, and X2 = sex led to the following model: y=547.65-2.85x1+10.67x2 For two children who spend the same amount of time eating, one male and one female, which child is predicted to consume more calories and by how much?
a. Develop the least squares estimated regression equation that relates labor hours to house square footage and type of flooring. b. Use the regression equation developed in part (a) to predict labor hours when the house size is 3350 square feet and the type of flooring is wood.
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations. A Minitab printout provides the following information. Predictor Constant Elevation Coef 315.00 -29.166 SE Coef 28.31 3.511 I 11.24 -8.79 P 0.002 0.003 S = 11.8603 R-Sq = 96.44 Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (c) The printout gives the value of the…
The accompanying table shows results from regressions performed on data from a random sample of 21 cars. The response (y) variable is CITY (fuel consumption in mi/gal). The predictor (x) variables are WT (weight in pounds), DISP (engine displacement in liters), and HWY (highway fuel consumption in mi/gal). The equation CITY - 3.17 +0.823HWY was previously determined to be the best for predicting city fuel consumption. A car weighs 2700 lb, it has an engine displacement of 1.6 L, and its highway fuel consumption is 35 mi/gal. What is the best predicted value of the city fuel consumption? Is that predicted value likely to be a good estimate? Is that predicted value likely to be very accurate? Click the icon to view the table of regression equations. The best predicted value of the city fuel consumption is (Type an integer or a decimal. Do not round.). Regression Table I R² Adjusted R2 WT/DISP WT/HWY Predictor (x) Variables P-Value WT/DISP/HWY 0.000 0.942 0.000 0.748 0.000 0.942 0.000…
Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x %3D where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct an 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. Lower limit: Upper limit:
Cellulon, a manufacturer of home insulation, wants to develop guidelines for builders and consumers on how the thickness of the insulation in the attic of a home and the outdoor temperature affect natural gas consumption. In the laboratory, it varied the insulation thickness and temperature. A few of the findings are: Monthly Natural Gas Consumption (cubic feet), Thickness of Insulation (inches), Outdoor Temperature (ºF), y x1 x2 30.3 6.0 40.0 24.2 12 40 27.9 8 49 On the basis of the sample results, the regression equation is: yˆy⁢^⁢ = 56.26 − 0.66x1 − 0.59x2 How much natural gas can homeowners expect to use per month if they install 6 inches of insulation and the outdoor temperature is 40 degrees F? (Round your answer to 2 decimal places.) What effect would installing 7 inches of insulation instead of 6 have on the monthly natural gas consumption (assuming the outdoor temperature remains at 40 degrees F)? (Round your answers…
A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation ŷ = 400-0.08x. Which of the following best describes the meaning of the slope of the least-squares regression line? (A) The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C) The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on…
In a snow geese feeding trial, a model was constructed relating gosling** weight change (Y), to digestion efficiency (X1) which is measured on a scale from 1 to 10, depending on how well nutrition is absorbed by the goosling, and diet (either plants or duck chow). Using Bi, etc. to represent the coefficients of independent variables, and defining any independent variables you create and use, write out the following: [WRITE OUT THE FULL MODELS IN SINGLE EQUATIONS IN EACH SECTION BELOW, NOT BROKEN DOWN INTO SEPARATE SUB-EQUATIONS] Define your independent variables here a) a first order model that allows for different intercepts but the same slope for each diet b) a first order model that allows for different slopes and intercepts for each diet (c) a first order model that allows for different slopes and the same intercept for each diet

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