Consider a simple linear regression model, Y₁ = Bo + B₁X₁ + ₁ for i=1,2,...,n with the usualrandom error term (&) assumptions. Suppose that hypotheses Ho: P₁ = 0 against H₁:₁ <0were tested and Ho: B₁ = 0 was rejected. Assume₁e₁² = 0.eii) Briefly explain what the conclusion of the test means for the values of Y given the values ofX.-1ii) Draw an example of a scatter plot with the fitted regression line for the problem mentionedabove.iii) Calculate and interpret the correlation coefficient for the problem at hand.

If the null hypothesis H0: β1=0 is rejected in favour of the alternative hypothesis H1: β1<0, it…

Answered: Consider a simple linear 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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17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 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…
A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[¹] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and 0 otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender What is the numerical value of b?
If Linear correlation coefficient r = 0.794556 Coefficient of determination = 0.631319 Equation of regression line is y = 16.5523 + %3D 0.725938x then both variables are moving in the same direction. A True В False
Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
3) For a sample of 306 students in a basic business communications course, the sample regression line y = 58.813 + 0.2875x was obtained. Here y = final student score at the end of the course x = score on a diagnostic writing skills test given at the beginning of the course The coefficient of determination was 0.1158 and the estimated standard deviation of the estimator of the slope of population regression line was 0.04566. a) Define and interpret the estimates of the regression equation. b) Interpret the coefficient of determination. c) What will happen to the final student score if his diagnostic writing test score increases by 2? d) How can you inmprove this model?
Suppose x1 ans x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
In a study, the simple linear regression equation was found as y = - 2.65 + 3.23 * x. Accordingly, if the value of x is 1.55, what will be the value of "y"? Biraraştımada basit doğrusal regresyon denklemi y-265+3,23xolarak bulunmuştur. Buna yöre xin değeri 1,55 olursa y'nin değeri ne olur?- 25 - O A) -2,36 O B) 2,36 O C) 6,32 O D) -7,66 O E) 7,66
Suppose that you have estimated coefficients for the regression model Y = B₁ + B₁X₁ + ß2X2 + ß3X3. Test the hypothesis that all three of the predictor variables are equal to 0, given the analysis of variance shown on the right. Use α = 0.05. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. Choose the correct null and alternartive hypotheses below. A. Ho: B₁ B₂ =B3 = 0 H₁: at least one ß; #0 C. Ho: B₁ B₂ = 3 = 0 H₁: B₁0, B₂0, B3 > 0 Find the critical value. The critical value is (Round to two decimal places as needed.) Source Regression Residual Error DF SS 3 9,654 23 2,400 B. Hō: at least one ß; ‡0 H₁: B₁ =B₂ =B3 = 0 D. H₁: B₁ = P₂ = ³3 = 0 H₁: B₁ B₂ B3 0 MS
Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁
2. We performed a linear regression using 25 observations. From the regression output we find that bo = 5.7, bị = 12.9, x = 11.4, Sz = 3.2 and MSE = 12.25. a. From the least squares line, what is the predicted response when x* = 10.65? y = b. What is the 95% confidence interval for the mean response when x* = 10.65? c. What is the 95% prediction interval for an individual response when x* = 10.65? d. Which interval is wider? The confidence interval or the prediction interval? O a. Confidence Interval b. Prediction Interval
Suppose x1 and x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
Consider a randomized block design involving three treatments and two blocks. Define all variables. X1 X2 Treatment 1 2. 1 3 Let x, = 0 if ---Select-- v is in effect and 1 if --Select--- v is in effect. Write a multiple regression equation that can be used to analyze the data. E(y) =

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