Concept explainers
Let x and y be random variables of the continuous type having the joint
Draw a graph that illustrates the domain of this pdI.
(a) Find the marginal pdfs of X and Y.
(b) Compute
(c) Determine the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?
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Probability And Statistical Inference (10th Edition)
- The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02arrow_forwardUse the general equation for the least square regression line to show that this line always passes through the point (x,y) * bars above the x and y.That is, set x=x(with a bar above the x) and show that the line predicts that y=y (with a bar above the y).arrow_forwardWhich pair of data points are always on the regression line: Y = a + bx? (0, 0) (0, b) (X, Y) (a,0)arrow_forward
- A Perodua dealer has hired you to analyze automobile demand in 30 regional markets for MyVi Model. A regression analysis was conducted using the following model. Q, = a + b, P, + b, Y +b, P + b, A Where, Q, = quantity demanded per year of MyVi automobiles. P,= average price of MyVi automobiles in thousands, (RM40) Y = household income in thousands, (RM24) P= average price of Kia Rio automobiles in thousands, (RM45) A = advertising expenditures per year in thousands, (RM400) The results of the computer analysis based on data collected in 30 regional markets are shown below: Variable Coefficient Std Error t-statistics Intercept 2,000 1000 2.00 Pp -10 2.5 -4.00 Y 0.025 0.02 1.25 PM 1.5 3.33 А 0.0825 0.025 3.3 Coefficient of determination, R = 0.96 %3D Standard error of estimate, SEE = 5.0 c) Based on 95% confidence level, identify the independent variables which can significantly influence demand for MyVi (t 2s. a s005 = 2.06). d) Calculate the price elasticity of demand. Would a…arrow_forwardFind the least-squares regression line ŷ = bo + b1r through the points %3D (-1,2), (2, 6), (5, 13), (7, 20), (10, 23), and then use it to find point estimates y corresponding to x = 3 and x = 6. For = 3, y = %3D For I = 6, y = %3Darrow_forwardFind the equation y = Bo + B1x of the least-squares line that best fits the given data points. (0,1), (1,1), (2,5), (3,5) The line is y =+ (Ox. (Type integers or decimals.)arrow_forward
- bx Find the curve of best fit of the type y = ae^ to the following data by the method of Least Squares. X y 1 10 5 15 7 12 9 15 12 21arrow_forwardFind the least-squares regression line ŷ = ba + b₁ through the points (−2, 2), (3, 6), (5, 14), (8, 19), (10, 27), and then use it to find point estimates corresponding to x = 1 and x = = 7. For x = 1, y = For x = 7, y =arrow_forwardSuppose we run a regression of Y on X using the following data points( xy)in a sample: (0, 1,(1,2).(-10, 9). What is the OLS regression line and what is the RSS? A:1+2X, RSS=3 B:1+X, RSS=0 C:2+X, RSS=-1 D:2+X, RSS=0arrow_forward
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