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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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.
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?
The accompanying table provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it best? Is the best regression equation a good regression equation for predicting the nicotine content? Why or why not? Tar Nicotine CO4 0.5 416 1.0 1817 1.1 1813 0.7 1713 0.7 1814 0.9 1415 1.1 1615 1.2 1615 1.2 149 0.7 1214 0.7 1813 0.8 1813 0.8 1915 1.1 162 0.2 314 1.1 1715 0.9 1514 0.8 1814 1.1 1614 0.9 1716 1.1 1414 1.0 167 0.6 717 1.3 1514 1.1 14
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…
The following data shows memory scores collected from adults of different ages. Age (X) Memory Score (Y) 25 10 32 10 39 9 48 9 56 7 Use the data to find the regression equation for predicting memory scores from age. The regression equation is: Ŷ = 4.33X + 0.11 Ŷ = -0.11X + 4.33 Ŷ = -0.11X + 13.26 Ŷ = -0.09X + 5.4 Ŷ = -0.09X + 12.6 Use the regression equation you found in question 6 to find the predicted memory scores for the following age: 28 For the calculations, leave two places after the decimal point and do not round: Use the regression equation you found in question 6 to find the predicted memory scores for the following age: 43 For the calculations, leave two places after the decimal point and do not round: Use the regression equation you found in question 6 to find the predicted memory scores for the following age: 50 For the calculations, leave two places after the decimal point and do not round:
The estimated regression equation for a model involving two independent variables and 10 observations follows. ý = 22.1370 + 0.5303Xq + 0.4920X2 (a) Interpret b₁ in this estimated regression equation. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₁ = 0.5303 is an estimate of the change in y corresponding to a 1 unit change in x₁ when X₂ is held constant. O b₁ = 22.1370 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. O b₁ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₁ when x₂ is held constant. Interpret b₂ in this estimated regression equation. O b₂ = 0.4920 is an estimate of the change in y corresponding to a 1 unit change in x₂ when x₁ is held constant. O b₂ = 22.1370 is an estimate of the change in y corresponding to a…
The accompanying table provides data for tar, nicotine, and carbon monoxide (CO) contents in a certain brand of cigarette. Find the best regression equation for predicting the amount of nicotine in a cigarette. Why is it best? Is the best regression equation a good regression equation for predicting the nicotine content? Why or why not? Tar Nicotine CO4 0.5 415 1.0 1916 1.1 1714 0.9 1713 0.7 1815 1.1 1315 1.1 1715 1.1 1614 1.0 169 0.7 1313 0.7 1813 0.7 1813 0.8 1714 1.0…
Consider the following regression equation representing the linear relationship between the Canada Child Benefit provided for a married couple with 3 children under the age of 6, based on their annual family net income: ŷ =121.09−0.57246xR2=0.894 where y = annual Canada Child Benefit paid (in $100s) x = net annual family income (in $1000s) Source: Canada Revenue Agency a. As the net annual family income increases, does the Canada Child Benefit paid increase or decrease? Based on this, is the correlation between the two variables positive or negative?The Canada Child Benefit paid .The correlation between the two variables is .b. Calculate the correlation coefficient and determine if the relationship between the two variables is strong, moderate or weak.r= , the relationship is . Round to 3 decimal places c. Interpret the value of the slope as it relates to this relationship. For every $1 increase in annual family net income, there is a $0.57246 decrease in…

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