Project #88902 - Applied Linear Statistical Models

 

Directions: Turn in all software output that is relevant. I do not need to see everything, just what

is necessary to solve a problem..Hand in problems in the correct order. Give handwritten or

typed explanations for each problem. I do not want to see just software output handed in.

Your explanations and corresponding software output should be contiguous.  Circle any important R output. Data set is attached. They will also be posted on Blackboard under ‘Course Materials’. Assume that all assumptons of the normal error regression model are met unless stated otherwise. In all hypothesis testing problems, state any conclusions.

 

Please make sure the data was read correctly.

 

 

#1. 

The height of soapsuds in a dishpan is of interest to soap manufacturers. An experiment

was performed by varying the amount of soap and measuring the height of the suds in a

standard dishpan after a fixed amount of agitation.  The data is given below. It is also available on Blackboard under ‘Course Materials’.  Here, X = amount of soap product(grams),  Y = height of suds(mm).

 

 

(a) Find the least squares regression line. Do a scatter plot.

(b) Test for a linear association between soap amount and height at an 0.05 level of significance.

Do this in two ways. Use a t-test and an F test. Use these two values to check that you did not make an error. (Verify F is the square of the appropriate t value).

(c) Test if there is an increasing linear association at the 0.05 level. Explain why an F test is not

appropriate here as it was in part (b) above.

(d) Give a 95% confidence interval(confidence limits) for mean height of soap suds for a soap amt. of  5.2 grams.

(e) Give a 95% prediction interval for the single height of soap suds for a soap amt. of 5.2 grams.

(f)  Give an unbiased point estimate of the error variance.

(g) Compute R and interpret it .

(h) Test the hypothesis that soap amt. and height are independent at the 0.01 level. Use the

sample correlation coefficient in your solution.

(i) Give a 98% C.I. for the population correlation coefficient, assuming a bivariate normal

distribution for soap amt. and height.

(j) Compute the residuals for the first two data points only.

(k) Give the ANOVA table.

(l) Find the Box-Cox prediction equation.Give the value of the best data.

(m) Is the Box-Cox transformation necessary for this data? Explain.

 

 

#2. (12 points)

In Problem 2.56, page 96, what does:

(a)   Chebyshev’s Theorem say about P( 33.2 < Y < 36.8) when X = 10?

(b)   Chebyshev’s Theorem say about P(Y > 43.0) when X = 12?

 

 

 

 

 

#3. (12 points)

    

(a)   Conduct the correlation test of normality for the data in Problem 1..Use a 5% level.

 

(b)   Optional three points extra credit.Use the Gruss inequality to explain why the correlation computed in (a) must be nonnegative.

 

 

 

#4. (6 points)

Explain why simple linear regression would be inappropriate in the following situation:

 

X = car speed,  Y = gas mileage

 

 

 

 

 

 

 

 

Data set for Problem 1..

 

Soap amt.      Height

 

  4.0                 33

  4.5                 42

  5.0                 45

  5.5                 51

  6.0                 53

  6.5                 61

  7.0                 62

Subject Mathematics
Due By (Pacific Time) 10/28/2015 12:00 am
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