Use multiple linear regression to fit
x1 0 0 1 2 0 1 2 2 1
x2 0 2 2 4 4 6 6 2 1
y 14 21 11 12 23 23 14 6 11
Compute the coefficients, the standard error of the estimate, and
the
correlation coefficient.
4. (35 points) Use multiple linear regression to fit the following experimental data, 12 1 4 5.5 1.5 5 y 13 22 16 9 9 (a) Compute the coefficients, the coefficient of determination , the standard deviation Sy, and the standard error of the estimate S/. Show your calculations. (b) Write a MATLAB script that solves part (a).
Q4.. [40 points] Consider the multiple linear regression model given by y - XB -+ s, where y and e are vectors of size 8 × 1, X ls a matrix of size 8 x 3 and Disa vector of sze 3 × 1. Also, the following information are available e = 22 y -2 and XTy 3 1. [10 points) Estimate the regression coefficients in the model given above? 2. [4 points] Estimate the variance of the error term...
True or false?: 1) If X and Y are standardized, then fit a linear regression line of standardized Y on standardized X, correlation between X and Y equals the slope of regression line. 2) If one calculates r for a set of numbers and then adds a constant to each value of one of the variables, the correlation will change. 3) The easiest way to determine if a relationship is linear is to calculate the regression line. 4) If the...
Linear Regression and Prediction perform a linear regression to determine the line-of-best fit. Use weight as your x (independent) variable and braking distance as your y (response) variable. Use four (4) places after the decimal in your answer. Sample size, n: 21 Degrees of freedom: 19 Correlation Results: Correlation coeff, r: 0.3513217 Critical r: ±0.4328579 P-value (two-tailed): 0.11837 Regression Results: Y= b0 + b1x: Y Intercept, b0: 125.308 Slope, b1: 0.0031873 Total Variation: 458.9524 Explained Variation: 56.6471 Unexplained Variation: 402.3053...
True or false: 1) If X and Y are standardized, then fit a linear regression line of standardized Y on standardized X, correlation between X and Y equals the slope of regression line. 2) If one calculates r for a set of numbers and then adds a constant to each value of one of the variables, the correlation will change. 3) The easiest way to determine if a relationship is linear is to calculate the regression line. 4) If the...
Assignment 2 PART 1. 1. Use the dataset below to run a regression where x1 and x2 are the independent variables and y is the dependent variable. y x1 x2 2 10 9 88 5 6 19 10 6 18 5 2 30 3 2 What is b1 (the coefficient on x1) for this regression? Round your answer to four decimal places. 2. Use the dataset below to run a regression where x1 and x2 are the independent variables and...
Use the following linear regression equation to answer the questions. x1 = 1.4 + 3.7x2 – 8.3x3 + 1.8x4 (c) If x2 = 2, x3 = 6, and x4 = 10, what is the predicted value for x1? (Use 1 decimal place.) Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1? Suppose x2 increased by 2 units. What would be the expected change in...
Use the data below to answer questions 1 to 6. Use a multiple linear regression model with linear main effects only. Show all calculations. No credit will be given for computer output x1 7.2 8.1 9.8 12.3 12.9 Sum 50.3 Sum of Squares 531.19 F11 4 5 6 7 8 9 E FR Calculate a 95% interval estimate for the average value of y at the data point X1=0.5, x2-0. HTML Editor
Consider a multiple linear regression model Y; = Bo + B1Xi1 + B22:2 + 33213 + Blog(x14) + Ej. We have the following statistics for the regression Call: 1m formula = y “ x1 + x2 + x3 + log(x4) Coefficients: Estimate Std. Error t value Pr(>1t|) (Intercept) 154.1928 194.9062 0.791 0.432938 x1 -4.2280 2.0301 -2.083 0.042873 * x2 -6.1353 2.1936 -2.797 0.007508 ** x3 0.4719 0.1285 3.672 0.000626 *** x4 26.7552 9.3374 2.865 0.006259 ** Signif. codes: O '***'...
Consider a multiple linear regression model Y; = Bo + B1Xi1 + B22:2 + 33213 + Blog(x14) + Ej. We have the following statistics for the regression Call: 1m formula = y “ x1 + x2 + x3 + log(x4) Coefficients: Estimate Std. Error t value Pr(>1t|) (Intercept) 154.1928 194.9062 0.791 0.432938 x1 -4.2280 2.0301 -2.083 0.042873 * x2 -6.1353 2.1936 -2.797 0.007508 ** x3 0.4719 0.1285 3.672 0.000626 *** x4 26.7552 9.3374 2.865 0.006259 ** Signif. codes: O '***'...