Suppose that (Yi, X;) satisfy the least squares assumptionsA random sample of size n = 250 is drawn and yieldsỸ = 5.4 + 3.2X, R² = 0.26(3.1) (1.5)a. Test Ho: B = 0 vs. H¡: ß¡ # 0 at the 5% level.b. Construct a 95% confidence interval for Bi.c. Suppose you learned that Y, and X; were independent. Would you besurprised? Explain.

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Answered: Suppose that (Y, X;) satisfy the least…

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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In a regression based on 30 annual observations, U.S. farm income was related to four in- dependent variables-grain exports, federal government subsidies, population, and a dummy variable for bad weather years. The model was fitted by least squares, resulting in a Durbin- Watson statistic of 1.29. The regression of e on ŷ yielded a coefficient of determination of 0.043. (a) Test for heteroscedasticity. (b) Test for autocorrelated errors.
Consider the following data. X represents the independent variable and Y represents the dependent variable. Suppose we wish to construct a least square regression line. Question 1) Calculate B1 with triangle over top. 0.525 0.425 0.725 0.625 Question 2) Calculate B0 with triangle over top. 4.98 4.88 5.36 4.4 Question 3) What is the least squares regression line. Y = 4.98 + 0.425X Y = 0.425 + 4.98X Y = 0.525 + 4.88X Y = 4.88 + 0.525X X 0 3 4 5 12 Y 8 2 6 9 12
A researcher wanted to examine the effectiveness of Vitamin C on the number of colds a year. The researcher obtained a sample of adults and asked to take Vitamin C daily. The average number of colds a year among adults is known to have the average of μ = 3On the basis of this sample, can the researcher conclude that Vitamin C has an effect on the number of colds a year? Use alpha =.05 two-tailed test. Colds: 2,2,2,1,3,3,1,2 Conducta two-tailed test with alpha = .05. Q1: State your null and research hypotheses using complete sentences Q2: What is the df? Q3: What are the cut-off points Q4: What is the standard deviation? You can just include the answer for the mean, SS, and the standard deviation. No need to type your computation. Q5: What is the estimated standard error? Show your computation. Q6: What is the t-value? Show your computation. Q7: State your conclusion thoroughly.
#3. What is the least squares regression line for the following set of data? y-hat = 2.18x + 27.74 y-hat = 2.14x + 27.44 y-hat = 1.94x + 26.24 y-hat =1.86x + 26.28
Add to MyRegistry 9 Mail - sgorham@a.. Like father, like son: In 1906, the statistician Karl Pearson measured the heights of 1078 pairs of fathers and sons. The following table presents a sample of 6 pairs, with height measured in inches, simulated from the distribution specified by Pearson. Compute the least-squares regression line for predicting son's height (v) from father's height (x). Round the slope and y-intercept values to at least four decimal places. Father's Son's height height 73.6 74.9 66.7 68.8 70.1 73.3 72.3 71.9 73.6 76.5 69.3 71.4 Send data to Excel Regression line equation: Save For Later Submit Assignment Check Answer © 2021 McGraw Hill LLC. AlI Rights Reserved. Terms of Use Privacy Center
Suppose a doctor measures the height, x, and head circumference, y, of 8 children and obtains the data below. Thecorrelation coefficient is 0.944 and the least squares regression line is y = 0.199x + 11.982. Complete parts (a) and (b)below.Height, x27.5 25.5 26.25 25.25 27.5 26.25 26 27.25 27.25 27 27.25 ФHead Circumference, # 17.5 17.0 17.2 17.0 17.5 17.3 17.2 17.4 17.3 17.3 17.4(a) Compute the coefficient of determination, R?R?.% (Round to one decimal place as needed.)(b) Interpret the coefficient of determination and comment on the adequacy of the linear model.Approximately % of the variation inis explained by the least-squares regression model.According to the residual plot, the linear model appears to be (Round to one decimal place as needed.)
A repeated measures experiment investigates if people can tickle themselves. A mean difference of 3.04 milliseconds is found between the Tickled By Self (485.17ms) and Tickled By Experimenter (482.13ms) means for 9 participants (NB: conditions were counterbalanced). The sum of squares value was 110.40. What is the appropriate test statistic and what it its critical value (applying α = 0.05)? t ; 2.365 r; 1.96 z; 2.307 t; 2.307
9) We have a sample of 6 observations on exam scores and hours of study and would like to estimate the following relationship using the least-squares method: Score Bo+ B hours +e, We expect the score to increase with hours of study. Score Hours 80 90 85 65 50 80 12 14 11 10 8 11 Escore = 450, hours = 66,E hours. score = 5085, score= 34850, hours=746 Estimate the unknown parameters using the method of OLS and find the least-squares prediction equation. b. Calculate SSE, R', standard error of the residuals (s), and standard error of slope coefficient (s) Construct and interpret a 90% confidence interval for B. Predict the score of a student who studies 9 hours for the exam, and construct and interpret a 90% confidence interval using the predicted value (prediction interval). a. C.

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