8 8. Consider the multiple regression model to investigate the rèlationship between the number of fishes (Y) per section of the streamand the following independent variables: the dissolved oxygen (3< oxy <10, in mg/liter), the maximum depth (1 < maxdepth < 8, in ft),and the water temperature (5

Regression Analysis: A regression analysis is used for one of the following motives: forecasting the…

Answered: 8. Consider the multiple regression…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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The sweetness, y, of the fruit is supposed to be related to the average daily sunshine hours, x. The following data shows the sweetness of the same type of fruit at different locations (sunshine hours). Fit the data to a simple linear regression model. x: 5, 6, 7, 6, 6, 8, 7, 5. y: 9, 10, 10, 11, 12, 13, 12, 8. . Calculate SSE, SST, ² and R². And interpret R².
The data set was obtained from 21 days of operation of a plant for the oxidation of ammonia to nitric acid. It is desired to fit a multiple linear regression model to predict Y = stack loss which is 10 times the percentage of the ingoing ammonia to the plant that escapes from the absorption column unabsorbed, as Y = Bo + B1Xair.flow + B2 water.temp + B3 xacid.conc Air.Flow represents the rate of operation of the plant. Water.Temp is the temperature of cooling water circulated through coils in the absorption tower. Acid.Conc is the concentration of the acid circulating, minus 50, times 10. This is the result of the best subsets regression. |Summary of best subsets, variable(s): stack.loss (stt 151astackloss) Adjusted R square and standardized regression coefficients for each submodel Adjusted R square 0.898623 No. of Effects Air. Flow Water.Temp Acid.Conc. Subset No. 1 2 0.604950 0.402523 This is the result of the forward stepwise regression. Degr. of Freedom P to enter 0.000000 Effect…
The police department must determine the speed limit on a bridge such that the flow rate of cars is maximum per unit time. The greater the speed limit, the farther apart the cars must be in order to keep a safe stopping distance. Experimental data on the stopping distances d (in meters) for various speeds v (in kilometers per hour) are shown in the table. (a) Convert the speeds v in the table to speeds s in meters per second. Use the regression capabilities of a graphing utility to find a model of the form d(s) = as2 + bs + c for the data. (b) Consider two consecutive vehicles of average length 5.5 meters, traveling at a safe speed on the bridge. Let T be the difference between the times (in seconds) when the front bumpers of the vehicles pass a given point on the bridge. Verify that this difference in times is given by T = d(s)/s + 5.5/s . (c) Use a graphing utility to graph the function T and estimate the speed s that minimizes the time between vehicles. (d) Use calculus to…
The sweetness, y, of the fruit is supposed to be related to the average daily sunshine hours, x. The following data shows the sweetness of the same type of fruit at different locations (sunshine hours). Fit the data to a simple linear regression model. x: 5, 6, 7, 6, 6, 8, 7, 5. y: 9, 10, 10, 11, 12, 13, 12, 8. 1 Calculate Sty; SET; Syy. 2 Calculate the correlation between x, y. And interpret their relationship.
Consider the multiple regression model to investigate the relationship between the number of fishes (Y) per section of the stream and the following independent variables: dissolved oxygen (3 < oxy < 10, in mg/liter), maximum depth (1 < maxdepth < 8, in feet), and water temperature (5< temp < 20, in °C). The location of the stream was also considered (lowland and upland). Y-hat = 23.09 + 0.199*oxy + 0.3361*maxdepth +8.6730*temp + 3.8290* lowland. Which of the following is(are) TRUE about the estimated regression coefficient for location of the stream? 1. The location of the stream is a categorical variable, so it is represented by a dummy variable with upland stream as the reference variable. II. Holding other factors constant, the number of fishes in lowland is 3.8290 higher than upland streams. O A. I only O B. II only O C. Both I and II O D. Neither I nor II
A chemistry experiment is performed measuring the solubility of potassium chloride (KCl) in water at different temperatures. The goal was to determine if there is a linear relationship between the temperature of the water and how much KCl can dissolve, measured as grams per 100 milliliter (g/100mL). After the experiments were performed, the following data was collected with temperature being the independent x-variable and solubility being the dependent y-variable: Temperature (°C) x Solubility (g/100mL) y 10 31 20 33 30 37 40 41 50 42 Based on the data given for temperature and solubility of KCl and without doing any math yet, which of the following do you predict would best describe the relationship between these variables? A positive linear relationship (r close to 1) A positive linear relationship (r close to -1) A negative linear relationship (r close to 1) A negative linear relationship (r close to -1)…
A researcher believes that there is a linear association between the level of potassiumcontent (y) in milligrams and the amount of fiber (x) in grams in cereal. The regression line forthe data is computed to be: ŷ = 36+27x rate. It was also computed that r = .62 a. If a cereal has 4 grams of fiber, what is its predicted potassium content?
Is the number of calories in a beer related to the number of carbohydrates and/or the percentage of alcohol in the beer? The accompanying table has data for 35 beers. The values for three variables are included: the number of calories per 12ounces, the alcohol percentage, and the number of carbohydrates (in grams) per 12 ounces. a. Perform a multiple linear regression analysis, using calories as the dependent variable and percentage alcohol and number of carbohydrates as the independent variables. Let X1 represent alcohol percentage and let X2 represent the number of carbohydrates. (Round to four decimal places as needed.)
7. For the data in the following table, assume that the dependent variable changes linearly with respect to the independent variable, then do the following: a. Find the value of the slope, m, and give the units for the slope. I = income (x $1000) (independent E = annual home energy use (kWh) (dependent variable) variable) 0 (i) 2 12,000 4 (ii) 6 15,000 10 (iii)
The relationship between yield of maize, date of planting, and planting density was investigated in an article. Let the variables be defined as follows. y = percent maize yield x = planting date (days after April 20) z = planting density (plants/ha) The following regression model with both quadratic terms where x₁ = x, X₂ = Z, X3 = x² and x4 = 2² provides a good description of the relationship between y and the independent variables. y =a +B₁x₁ + B₂X₂ + B3X3+B₁x₁ + e (a) If a = 21.07, B₁ = 0.653, B₂ = 0.0022, B3 = -0.0207, and B4 = 0.00002, what is the population regression function? y = 509 X (b) Use the regression function in Part (a) to determine the mean yield for a plot planted on May 7 with a density of 41,182 plants/ha. (Give the exact answer.) (c) Would the mean yield be higher for a planting date of May 7 or May 23 (for the same density)? The mean yield would be higher for [May 7 You may need to use the appropriate table in Appendix A to answer this question.
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?
In the regression model Y =a, +a,X, +a,D, +a, (X, *D,)+u, %3D X is a continuous variable and D is dummy variable. What is a, ? a. is always positive Ob. indicates the difference in the slopes of the two regressions. c. is the difference in means in Y between the two categories. d. Indicates the difference in the intercepts of the two regressions.

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8. Consider the multiple regression model to investigate the rèlationship between the number of fishes (Y) per section of the stream and the following independent variables: the dissolved oxygen (3< oxy <10, in mg/liter), the maximum depth (1 < maxdepth < 8, in ft), and the water temperature (5