Consider a population regression equation:Y = B₁ + B₁₂X + U₁where B and B are the intercept and slope parameters, respectively. Assume that E(u) = 0.Note that the equation does not take into account yet the changes in the measurement of X.e. Show thatCov(X,Y)1 Var (X)B₁Given the measurement change in X, how will the following parameters change?f. Slope parameter, B₁g. Intercept parameter, B2Consider a random sample of (X, Y), with a sample size of n. How will the followingestimators change given the measurement change in X?h. Sample mean, xi. Sample variance,

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Answered: Consider a population regression…

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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Þata on the relationship between plant age and dry matter in the stalk are given in the Table. X (Age) 4 6 8 10 12 14 16 18 Y (Dry matter, %) 24 28 35 48 44 49 51 | 51 i) Express the relationship between the exhausted age and dry matter level with the regression equation (Ý = aX + b). ii) Using the obtained equation, estimate what the dry matter% of plants with ii) a age of 22 weeks will be. iii) By drawing the skater diagram, find the correlation coefficient and interpret the found values. iii)
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. ŷ = 18.6 + 3.7x, - 2.2x2 + 7.9x3 + 2.6x4 (a) Interpret b, in this estimated regression equation. = 3.7 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x3, and x, are held constant. = -2.2 is an estimate of the change in y corresponding to a 1 unit change in x, when x2, x3, and x are held constant. O b1 = 7.9 is an estimate of the change in y corresponding to a1 unit change in x, when x,, x2, and x, are held constant. O b, O b, = 3.7 is an estimate of the change in y corresponding to a 1 unit change in x, = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x3 are held constant. when and x4 are held constant. Interpret b, in this estimated regression equation. O b2 = 2.6 is an estimate of the change in y corresponding to a 1 unit change in x, when x,, x2, and x, are held constant. = 7.9 is an estimate…
Solids (grams) obtained from a material as y, with respect to drying time (Hours) as x. Ten experiments were carried out to obtain the following observations: Table on the picture (a) Create a scatter diagram for the data. (b) Estimated regression model according to the data conditions. (c) Calculate Model Accuracy (R²) and Relationship Between Variables (r²)
Use the computer output to estimate the intercept β0 and the slope β1.The regression equation is Y⁢=811-3.56X. Predictor Coef SE Coef T P Constant 811.183 88.17 9.20 0.000 X -3.562 1.168 -3.05 0.006 Intercept β0: Slope β1:
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.
You are given the following data, where X1 (final percentage in math class) and X2 (number of absences) are used to predict Y (standardized math test score in third grade): Y X1 X2 345 70 390 80 1 370 75 4 375 92 400 82 350 70 3 310 61 5 420 80 375 88 3 410 72 1 485 99 300 65 7 Determine the following multiple regression values. Report intercept and slopes for regression equation accurate to 3 decimal places: Intercept: a = Partial slope X1: bị = Partial slope X2: bz = Report sum of squares accurate to 3 decimal places: SSreg Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places): F-ratio = P-value = Report the variance of the residuals accurate to 3 decimal places: Sres = Report the results for the hypothesis test for the significance of the partial slope for final percentage in math class (report the test statistic for the regression coefficients accurate to 3 decimal places and P-value accurate to…
Q.4. Obtain the equation of the line of regression of y on x from the following data and estimate the blood pressure when the age is 50 years. Age in years x Blood pressure y 50 142 40 120 71 162 35 110 60 140 45 125 52 155 47 140 36 111 40 135 65 150 59 153
Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.
The following data on x maternal age in years of the young birth mothers and y = weight of baby born in grams summarizes the result of a study. Assume that a simple linear regression model y = Bo + B1x + e is an appropriate model for the study. x-bar = 17 (avg of x's) y-bar = 3004.1 (avg of y's) SSx = 20 SSxy %3D 4903 SSw 1539182.9 n 10 Calculate the value of s-(standard error of regression) and enter the answer to the nearest tenth (1 decimal place).
Given are five observations collected in a regression study on two variables. xi 2 6 9 13 20 yi 9 18 8 25 21 (b) Develop the estimated regression equation for these data. ŷ = (c) Use the estimated regression equation to predict the value of y when x = 13.
Calculate the standard error of the estimate of Y from the regression of Y on X for the following data: n= 10 E y- 90, Σw- 120. Ex - 200 where x-X-X, y-Y Y.
Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income: ŷ =121.09−0.57246xR2=0.894 where y = annual Canada Child Benefit paid (in $100s) x = net annual family income (in $1000s) Source: Canada Revenue Agency a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative?The Canada Child Benefit paid .The correlation between the two variables is .b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak.r= , the relationship is . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in…

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