Property 4: Regression Coefficients are Independent of theChange of the Origin but not the Change of Scale

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Answered: Property 4: Regression Coefficients are…

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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The figure shown to the right contains a scatter plot of 10 data points for trees, where the diameter of a tree at breast height (Dbh) is given in inches and the height is given in feet. The regression model is shown below, where x is the Dbh in inches and y is the height in feet. y = 0.91x +4.39 (A) Interpret the slope of the model. O A. The rate of change of height with respect to Dbh is 4.39 in/ft. O B. The rate of change of height with respect to Dbh is 0.91 ft/in. O C. The rate of change of height with respect to Dbh is 4.39 ft/in. O D. The rate of change of height with respect to Dbh is 0.91 in/ft. Height (ft) 40- 0 16 Dbh (in) 25
What is the interpretation of the intercept regression coefficient in a regression model? A. The change in X for a unit increase of Y B. The change in Y for a unit increase of X C. The estimated value of the dependent variable when X takes the value 1 D. The estimated value of the dependent variable when X takes the value 0
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The accompanying data are the length (in centimeters) and girths (in centimeters) of 12 harbor seals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a)x= 140 cm (b)x= 172 cm (c) x = 164 cm (d) x = 158 cm Click the icon to view the table of lengths and girths. The equation of the regression line is y=x+7 (Round to two decimal places as needed.). 4
Question 5 A regression diagnostic tool used to study the possible effects of collinearity is the slope. the Y-intercept. the VIF. O the standard error of the estimate.
Answer d,e and f
A high R2 is all that is needed to determine if a regression is a good model of a causal process. A. True B. False
To what part of the equation of the straight line < Y = MX + C > does the OLS regression coefficient correspond? - This question is based on Data Analysis A. YB. MC. XD. D
Using your dataset, run a regression of Y=GPA and X=# Friends.(do not need your actual data, just the regression results)a) State what this regression is attempting to analyze. “By running this regression, we areattempting to show.....”b) Write out the regression equation and describe what it shows (if Friends increase by 1, then. . . ).c) Find your hypothesized GPA when the # friends equals 17.d) Is the slope of # of Friends significantly different from zero?Include Ho, Ha, decision rule, t statistic from table, tc, decision, and conclusion.e) Is the r-squared of # of Friends significantly different from zero?Include Ho, Ha, decision rule, F statistic from table, Fc, decision, and conclusion.
The volume (in cubic feet) of a black cherry tree can be modeled by the equation y = - 50.8 + 0.3x, +4.5x,, where x, is the tree's height (in feet) and x, is the tree's diameter (in inches). Use the multiple regression equation to predict the y-values for the values of the independent variables. x, = 70, x, = 8.6 The predicted volume is cubic feet. (Round to one decimal place as needed.)
Cheick is investigating how long his phone's battery lasts (in hours) for various brightness levels (on a scale of 0-100). His data is displayed in the table and graph below. Brightness Level (x) Hours (y) 23 6.7 27 5.9 30 7.3 36 7.2 71 3.8 72 3.6 85 3.1 94 1.9 (a) Use the Corr/Regression to find the equation for the line of best fit. Round your answers to two decimal places. ˆy = 8.74 + -0.07x (b) Interpret the slope in context. Cheick expects the battery life to go down by 0.07 hours for each increase of 1 in the brightness level. Cheick expects the brightness to decrease by 0.07 for every hour that goes by. Cheick expects his phone battery to last 0.07 hours if he keeps the brightness level at 0. Cheick expects his phone battery to last 8.74 hours if he keeps the brightness level at 0. Correct (c) What does the equation predict for the number of hours the phone will last at a brightness level of 36? 6.2 hours Round your answer to…
The accompanying data are the length (in centimeters) and girths (in centimeters) of 12 harbor seals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x=140 cm (b) x=172 cm (c) x=164 cm (d) x=158 cm Length, x Girth, y138 106168 130153 116144 105159 126158 119124 103137 103154 121148 111147 106145 110 The equation of the regression line is y=____x + ___

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Property 4: Regression Coefficients are Independent of the Change of the Origin but not the Change of Scale