B. We have production data for 22 firms, from which the following summarystatistics are derived,nnny = 20, Σ(v₁ - y)² = 100, x= 10, Σ(x₁ - x)² = 60, Σ(x₁-x)(y₁ -) = 30i=1i=1=i=1where y = In output and x = labour hours input(i) Compute the least squares estimates of a and ß in the model,y = a + Bx + ε(ii) Estimate the output elasticity of labour(iii) Test the hypothesis that ß = 1.(iv) Form a 95% confidence interval for o², the variance of .Note: X² 0.025,2034.1696 and X² 0.975,202= 9.5908

The question related to regression analysis.The data on the production of the firmn=22 is the sample…

Answered: B. We have production data for 22…

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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4. We would like to determine how a man's weight can be used to predict his systolic blood pressure. We measure the weights (in pounds) and the systolic blood pressures of a sample of 17 men. The data are plotted on a scatterplot and it can be seen that a linear relationship is a reasonable assumption. The least squares regression line is calculated to be ŷ = 125.561 + 0.145x. The ANOVA table (with some values missing) is shown below: |Source of Variation | df | Sum of Squares Mean Square F Regression Error Total 26.46 617.82 (a) We would like to test whether a linear relationship exists between a man's weight and his systolic blood pressure. We will conduct an analysis of variance to test Ho: B1 = 0 vs. Ha: B1 + 0 at the 5% level of significance. Enter all missing values in the ANOVA table. Calculate the value of the test statistic, find the P-value of the test and provide a properly worded conclusion. (b) What is the value of the correlation between weight and systolic blood pressure…
The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game in 2018. Complete parts (a) through (f). Click here to view the data. Click here to view the critical values of the corelation coefficient (a) Find the least-squares regression line treating speed at which the ball was hit as the explanatory variable and distance the ball traveled as the response variable. y (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Begin by interpreting the slope. Data table O A. The slope of this least-squares regression line says that the distance the ball travels increases by the slope with every 1 mile per hour increase in the speed that the ball was hit. O B. The slope of this least-squares regression line shows the increase in the speed that the ball was hit with every 1 foot increase in the distance that the ball was…
16. A scatterplot of the monthly salary (in thousands of pesos) versus years of education for seven full-time workers is displayed below. The least- squares regression line is drawn on the plot. Six of the data points are plotted with open circles and the seventh is plotted with a solid circle. The data point plotted with a solid circle to 20 Ne stynan eftdutatien A. has a large residual and is influential. B. has a small residual and is influential. C. has a large residual and is not infiluential. D. has a small residual and is not influential. 00 09 oad jo umroy s
For theoretically modelling the economic development of national economy scenarios the following 2 models for GDP increment are analysed: a. Yt = Yt-1 + at b. Yt = 1.097 Yt-1 - 0,97 Yt-2 + at, where Y - GDP increment a - White noise with zero mean and constant variance o2 =100 t- Time (quarters starting with Q1, 1993) Check by an algebraic criterion which one is stationary.
Employee’s human capital is measured in terms of his/her age, education, tenure, and rank. Number of years an employee worked in the same organization measures the amount of firm-specific human capital that employee possesses. Data of 413 employees’ tenure was analyzed to predict interim leadership role importance in a study reported in Journal of Advanced Management Research (Vol. 9, 2012). The following table shows the data of these employees tenure in the organization: Tenure (in years) 0-1 1-6 6-11 11-20 20-21 No. of employees 48 109 58 75 123 Calculate mean tenure of these 413 employees.
Consider data on every game played by the Brooklyn Nets in 2014 (82 games) that includes the variables margin, - the Net's margin of victory (number of points the Nets scored minus the number of points their opponent scored) for game i, and • home; - a dummy variable equal to 1 when the Nets are the home team (game i was played in their home arena) and equal to 0 when they are the away team (game i was played in the opponent's arena). I use the least-squares method to estimate the following regression model margin = a + ßhome; + ei Below is the Stata output corresponding to the estimated regression line: regress margin home if team===== "Brooklyn Nets" . Source Model Residual Total margin home _cons SS 1459.95122 15252.0488 16712 df 1459.95122 1 80 190.65061 None of the above 81 206.320988 Coef. Std. Err. 8.439024 3.049595 -5.219512 2.156389 MS t Number of obs F(1, 80) Prob > F R-squared O The Nets lost more games than they won in 2014 P>|t| 2.77 0.007 -2.42 0.018 Adj R-squared = Root…
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Civil engineers often use the straight-line equation, y = bo+b ₁x, to model the relationship between the shear strength y of masonry joints and precompression stress, x. To test this theory, a series of stress tests were performed on solid bricks arranged in triplets and joined with mortar. The precompression stress was varied for each triplet and the ultimate shear load just before failure (called the shear strength) was recorded. The stress results for n = 7 resulted in a Coefficient of Determination of 0.7589. Given that r ²= 0.7589, give a practical interpretation of r 2, the coefficient of determination for the least squares model. In repeated sampling, approximately 75.89% of all similarly constructed regression lines will accurately predict shear strength. We expect about 75.89% of the observed shear strength values to lie on the least squares line. We expect to predict the shear strength of a triplet test to within about 0.7589 tons of its true value. About 75.89% of the total…
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.
Suppose Derrick is an insect enthusiast who measured the body length and weight of three insects in his backyard. His data are shown in the table. Length (mm) Weight (mg) Variable ?x ?y Insect 1 7 28 Insect 2 21 42 Insect 3 35 70 Derrick used the data to compute the least squares regression line. ?̂ =1.5?+15.167y^=1.5x+15.167 Calculate the residual value for each of Derrick's data points and the sum of the residual values. Report your answers precise to three decimal places. Residual 1: Residual 2: Residual 3: Sum of the residuals:
Use the following data for parts (a) through (e). x 5 7 3 16 12 9 y 8 9 11 27 15 13 Determine the equation of the least squares regression line to predict y by x. y^ = (value rounded to 4 decimal places ?) + (value rounded to 4 decimal places ?) x

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