Consider a set of data (x₁, y₁), i = 1, 2, ..., n and the simple linear regression model given by:Yi Bo + B₁x₁ + εiwith E() = 0, Var(ɛ;) = o² and all &;'s are independent and normally distributed.Suppose further that a random sample of size 10 is selected and the fitted regression equation isobtained:with SB₁b)= 0.071 and SSxx = 1568.625.a)If we were to draw a scatter plot for the data, what kind of relationship would be expected?Justify your answer.Construct analysis of variance (ANOVA) and use it to test at 5% level whether or not there isa significant relationship between x and y.Verify the results in b) using a 95% confidence interval.c)ŷi = 2.106 -0.933x₁

The regression line is: y^i=2.106-0.933xi. It is given that: sβ^1=0.071 (i.e., the standard error of…

Answered: Consider a set of data (x,y), i = 1, 2,…

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 that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 12 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.85, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 85000 and the sum of squared errors (SSE) is 15000. From this information, what is SSE/SST? (a) .2 (b) .13 (c) NONE OF THE OTHERS (d) .15 (e) .25
Suppose 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=0
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.72, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 72000 and the sum of squared errors (SSE) is 28000. From this information, what is MSE/MST? (a) .4000 (b) .3000 (c) .5000 (d) .2000 (e) NONE OF THE OTHERS
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual model…
Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 21 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.8, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 80000 and the sum of squared errors is (SSE) 20000. From this information, what is the value of the hypothesis test statistic for evidence that the true value of the coefficient of the second explanatory unknown exceeds 5? (a) 4 (b) 3…
Find the simple regression line y=α+βx for the pairs of points belonging to the independent and dependent variables (xi,yi) , respectively. Also, interpret the result by calculating the Pearson correlation coefficient.
Show the best fitted line on scatter diagram and Find the predicted value for each y using the exposure time and the equation obtained in part b (b. Find the equation of regression line between radiation doses on exposure time .usingleast square method)
Find the least square regression line for the data points : (1,1), (2,3). (4,5).
The number of murders and robberies per 100,000 population for a random selection of states are shown. Find the equation of the regression line y'=ax+b, and predict the number of robberies when x=4.5 murders murders,x: 2.4,2.7,5.6,2.6,2.1,3.3,6.6,5.7 robberies,y : 25.3,14.3,151.6,91.1,80,49,17.3,45.8
The model developed from sample data that has the form of Yhat = bo +bjX is known as the multiple regression model with two predictor variables. (True or False) O True O False
A trucking company considered a multiple regression model for relating the dependent variable of total daily travel time for one of its drivers (hours) to the predictors distance traveled (miles) and the number of deliveries of made. After taking a random sample, a multiple regression was performed and the output is given below. Interpret the slope of the deliveries variable. When deliveries increases by 0.805 units, time increases by 1 hour, holding all other variables constant. 2) We do not have enough information to say. 3) When deliveries increases by 1 unit, time decreases by 0.805 hours, holding all other variables constant. 4) When deliveries decreases by 1 unit, time increases by 0.805 hours, holding all other variables constant. 5) When deliveries increases by 1 unit, time increases by 0.805 hours, holding all other variables constant.
The least squares regression line for a set of data is calculated to be y = 24.8 + 3.41x. (a) One of the points in the data set is (4, 37). Calculate the predicted value. (b) For the point in part (a), calculate the residual.

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