The following table shows data on X= pressure of extracted gas (microns) and Y= extraction time (min). Assume Y is normally distributed with constant variance o? for each x. 155 160 260 275 325 370 420 480 3.1 3.3 3.7 40 130 2.5 3.0 4.1 4.3 4.8 5.0 5.4 4. Do a test of linear regression model utility at a= 0.01 (Using 5 steps). 5. Calculate a point estimate of the true average extraction time when the pressure of extracted gas is x*= 500 microns, then calculate a 95% PI for a future value of extraction time when the pressure of extracted gas is x*= 500 microns. 6. Calculate and interpret the sample correlation coefficient r, then test (Using 5 steps) for the absence of correlation between extraction time and pressure of extracted gas at a = 0.05. Note the Steps are: Step 1. Hypotheses and significance level: Но: a = Step 2. Test Statistic and its sampling distribution under Ho: Step 3. Observed value of the test statistic: Step 4. P-value under Ho: Step 5. Decision and conclusion (interpretation of the result):

The following table shows data on X= pressure of extracted gas (microns) and Y= extraction time (min). Assume Y is normally distributed with constant variance o? for each x. 155 160 260 275 325 370 420 480 3.1 3.3 3.7 40 130 2.5 3.0 4.1 4.3 4.8 5.0 5.4 4. Do a test of linear regression model utility at a= 0.01 (Using 5 steps). 5. Calculate a point estimate of the true average extraction time when the pressure of extracted gas is x= 500 microns, then calculate a 95% PI for a future value of extraction time when the pressure of extracted gas is x= 500 microns. 6. Calculate and interpret the sample correlation coefficient r, then test (Using 5 steps) for the absence of correlation between extraction time and pressure of extracted gas at a = 0.05. Note the Steps are: Step 1. Hypotheses and significance level: Но: a = Step 2. Test Statistic and its sampling distribution under Ho: Step 3. Observed value of the test statistic: Step 4. P-value under Ho: Step 5. Decision and conclusion (interpretation of the result):

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.1: Functions Of Several Variables

Problem 34E: The following table provides values of the function f(x,y). However, because of potential; errors in...

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The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02
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