An engineer measures a dependent variable y and independent variables x1, x2,and x3.MINITAB output for the model y = Bo + B1X1 + B2X2 + B3X3 + ɛ is presented as follows.The regression equation isY= 0.367 + 1.61 xi - 5.51 X2 + 1.27 X3Predictor Coef SE Coef T PConstant 0.3692 0.92310.400.698X11.6121 1.3395 1.210.254X25.5049 1.4959 3.68 0.004XЗ1.2646 1.97600.64 0.537Of the following, which is the best next step in the analysis? Explain your reasoning.i.Add interaction terms x¡x2 and x2x3 to try to find more variables to put into the model.ii. Add the interaction term x,×3 to try to find another variable to put into the model.iii. Nothing needs to be done. This model is fine.iv. Drop x1 and X3, and then perform an F test.V.Drop x2, and then perform an F test.vi. Drop the intercept (Constant), since it has the largest P-value.

From the given regression output, the p-values of x1 and x3 are greater than 0.05. Hence, these two…

Answered: An engineer measures a dependent…

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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Suppose there is 1 dependent variable (dissolved oxygen, Y) and 3 independent variables (water temp X1, depth X2, and hardness of water X3). Below is the result of the multiple linear regression.Which of the following is the equation of the multiple regression model? Y = 4.36 + 0.37X1 + 0.24X2 + 0.04X3 Y = 0.00 + 0.02X1 + 0.56X2 + 0.37X3 Y = 24.84 - 1.17X1 - 0.15X2 - 0.04X3 Y = 5.69 – 3.20X1 - 0.61X2 -0.95X3
Laetisaric acid is a compound that holds promise for control of fungus diseases in crop plants. Below is the least-squares regression equation to predict fungus growth (mm) from laetisaric acid concentration (µG/ml): ŷ =31.8 -0.712x Which of the following statements is correct? A. Above-average values of laetisaric acid concentration tend to accompany above-average values of fungus growth. B. From the given regression equation, we know the correlation is negative and we can say what the exact value of that correlation is. C. When fungus growth increases by 1 mm, the laetisaric acid concentration decreases by 0.712 µG/ml. D. None of the above.
Report the equation of the regression line and interpret it in the context of the problem
Find the multiple regression equation with weight as the response variable and the dummy variable of sex and the variable of age as the explanatory variables.
i. Determine the dependent and independent variable ii. Based on the output, state the simple linear regression model. ii. Interpret the linear regression model obtained in part (b).
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?
At a large state university, the Statistics department is interested in tracking the progress of its students from entry until graduation. In this example: X represents a student’s final numeric grade (out of 100) in an introductory statistics course Y represents a student’s final numeric grade (out of 100) in an upper-level statistics course The least-squares regression equation for this relationship is: Y = 5.20 + 0.93X What is the slope of the regression line? Provide a numeric value as shown in the equation.
An advertising firm wishes to demonstrate to potential clients the effectiveness of the advertising campaigns it has conducted. The firm is presenting data from 12 recent campaigns, with the data indicating an increase in sales for an increase in the amount of money spent on advertising. In particular, the least-squares regression equation relating the two variables cost of advertising campaign (denoted by x and written in millions of dollars) and resulting percentage increase in sales (denoted by y) for the 12 campaigns is y = 6.18 +0.14x, and the standard error of the slope of this least-squares regression line is approximately 0.10. Using this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B₁. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed…
When using population size as the explanatory variable, x, and broadband subscribers as the response variable, y, for data on the number of individuals in a country with broadband access and the population size for 36 nations, the regression equation is y = 4,975,098 +0.0342x. a. Interpret the slope of the regression equation. Is the association positive or negative? Explain what this means. b. Predict broadband subscribers at the (i) population size 7,014,655, (ii) population size 1,155,173,053. c. For one nation, y = 71,110,000, and x = 322,413,902. Find the predicted broadband use and the residual for this nation. Interpret the value of this residual. a. Since the association is positive, the slope means that as the (Type an integer or a decimal.) b. (i) The predicted broadband subscribers for population size 7,014,655 is (Round to the nearest whole number as needed.) population size increases by 1 unit, the number of broadband subscribers tends to increase by 0.0342.

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