From laboratory tests, the relationship between stress (0) and strain (ɛ) is obtained as shown in the tablebelow:Stress (0)Strain(ɛ)15980.000952980.00271980.003178980.004790980.006107980.0085a. Make an exponential regression equation from the data aboveb. Find the correlation coefficient

Given data Stress (σ) Strain (ε) 1598 0.0009 5298 0.002 7198 0.0031 7898 0.0047 9098…

Answered: From laboratory tests, the relationship…

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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c) Show that the coefficient of determination, R², can also be obtained as the squared correlation between actual Y values and the Y values estimated from the regression model where Y is the dependent variable. Note that the coefficient of correlation between Y and X is Eyixi r = And also that ỹ = ŷ (18.75)
Working as a professor, I may want to try and predict success on a final exam by student success on exam 1 and see whether or not there is a relationship between those. I gather data from a set of students and obtain their first exam score and their final exam score. Using the following data, find the Pearson’s r correlation coefficient, produce a linear regression equation, and describe the associated R2 value. First exam score (X) Final exam score (Y) 95 100 90 92 95 90 85 90 85 85 80 75 65 75 60 50 70 82 90 95 80 100 90 90 75 60 75 80 Pearson’s r = ______________ Is the r significant? _______________ Linear regression equation: ____________________
A regression was run to determine if there is a relationship between hours of study per week (x) and the final exam scores (y).The results of the regression were: y=ax+b a=5.088 b=26.56 r2=0.913936 r=0.956 Use this to predict the final exam score of a student who studies 4.5 hours per week, and please round your answer to a whole number.
Measurements of the electrical resistivity of tungsten at specified temperatures are presented in the table below. The error in the determination of the temperature was negligible. The temperatures are stated as absolute temperatures in °K. The units of resistivity are u Ncm . Carry out a regression analysis for resistivity as a function of temperature. Temperature Resistivity 300 5.54 Include a scatterplot showing the residuals vs temperature. 400 7.95 Do the regression assumptions appear to be valid? 500 11.00 600 12.28 Include a scatterplot showing the raw data points as black circles as well as a continuous blue line representing the regression model. 700 15.95 800 18.46 Find the lower and upper limits for a 99% confidence interval for the slope of the regression model. Add a pair of red lines to the scatterplot: both passing through the centroid of the data, one having the slope corresponding to the lower bound of the confidence interval, and the other having the slope…
A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = 15; SSx = 3; My = 7; Mx = 3 What is b equal to (Please include the sign: e.g., -20)? What is a equal to (please include the sign: e.g., +4.0)? Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?
Question: Give the equation of the model you chose in (b ) using the transformed variables .
A researcher investigates the relationship between cigarette smoking (X) and work absences (Y). The number of cigarettes smoked daily and the number of days absent from work due to illness are collected for N= 12 employees. The preliminary results are below: What is the regression equation? How many absences (Y) would expect someone who smokes X = 10 cigarettes a day to have?
For half-life demonstration, plot ln(half-lives) in the x-axis vs ln(no. of “tails-up” coins) in the y-axis. Perform linear regression to obtain the value of the slope, the value of the y-intercept, and the correlation coefficient r. What is the significance of these values?
The mortality rate of a sample of the population as a function of daily tobacco consumption can be seen below: Number of cigarettes "x": 3 5 6 15 20 Mortality rate "y" : 0.2 0.3 0.4 0.5 0.7 With these data, solve the following: a. Determine and interpret the correlation coefficient. b. Find the regression line of y on x. c. What will be the mortality rate for a consumer of 40 cigarettes per day?
From the results shown above, write the regression equation.
3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁; −0.047X2; +0.032X3; −0.018X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic=1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁₁ = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X31 Price of wine and sprits in year t (index number with 2001 = 100) = X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw…
3. Regression analysis breaks scores on the DV into... (explain and give equations)

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