HW5The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year’s usage and temperatures are in the following table:MonthTemp.Usage/1000MonthTemp.Usage/1000Jan.21185.79July.68621.55Feb.24214.47Aug.74675.06Mar.32288.03Sept.62562.03Apr.47424.84Oct.50452.93May50454.58Nov.41369.95June59539.03Dec.30273.93Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). What is the estimate of ?What is the estimate of expected stem usage when the average temperature is 55 F?What change in mean stem usage is expected when the monthly average temperature changes by 1 F?Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual.Test for significance of regression using α=0.01 (Use ANOVA).Calculate the r2 of the model.Find a 99% CI for .

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

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HW5

The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year’s usage and temperatures are in the following table:

Month	Temp.	Usage/1000	Month	Temp.	Usage/1000
Jan.	21	185.79	July.	68	621.55
Feb.	24	214.47	Aug.	74	675.06
Mar.	32	288.03	Sept.	62	562.03
Apr.	47	424.84	Oct.	50	452.93
May	50	454.58	Nov.	41	369.95
June	59	539.03	Dec.	30	273.93

Assuming that a simple linear regression model is appropriate, fit the regression model relating stem usage (y) to the average temperature (x). What is the estimate of ?
What is the estimate of expected stem usage when the average temperature is 55 F?
What change in mean stem usage is expected when the monthly average temperature changes by 1 F?
Suppose that the monthly average temperature is 47 F. Calculate the fitted value of y and the corresponding residual.
Test for significance of regression using α=0.01 (Use ANOVA).
Calculate the r²of the model.
Find a 99% CI for .

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Part A of question one asks for the variance (sigma squared), not the equation of regression line. Is the variance 2.79 as I listed on my answer sheet?

Maybe my image didn't go through, but I already had the answer to subparts B and C to the question, which you list as #2 and #3.

But I need help with parts D, E, and F.

I have the following answers for D.

d. Y hat (fitted value = 426.46), with residual of -1.62.

e. r squared value = 1.00

g. 99% confidence interval = (-11.63, -1.05)

Thanks

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