Prediction Bands

“Tungsten shields” (simple linear regression)
Tungsten steel erosion shields are fitted to the low-pressure blading in steam turbines. The most important feature of an erosion shield is its resistance to wear. This is difficult, expensive and destructive to measure directly in terms of abrasion loss, but it is known to be associated with the hardness of steel. Measuring hardness is relatively easy and can be carried out at points on less critical areas of the shields that will not affect the shield’s performance. An engineer measures both the abrasion loss and the hardnesses of 25 erosion shields. Each shield was taken at random from a different batch and can be assumed to form a random sample.

The data is available on iLearn in the Assignments directory (as .mtw, .txt and .xls). Use Minitab to obtain the relevant output to answer the following.
Print your output on to A4 paper and submit at the back of your assignment.

(a) Obtain a scatterplot of the data AND a scatterplot of the data with the regression line.
(b) Obtain the output for the regression of Abrasion Loss (Y) on Hardness (x).
In MTB11, use STAT > Regression > Fit regression model
Response: ‘Abr.Loss’ , Continuous predictors: Hardness , Model: default , Graphs:  4 in 1
(c) Identify and label (highlight or circle by hand) each of the following in the output:
dfReg , dfErr , dfErr , SSReg, SSErr, SSTot, MSE (ignore “Lack-of-fit” and “Pure-error”)
S , R 2 , a , b , se(b) , t and p-value for b
(d) Include the residual diagnostics plot and comment on any problems.
(e) Obtain the plot with both the confidence and predictions bands (both at 95%).
In MTB11, use STAT > Regression > Fitted line plot > Linear > Options >
 Display confidence interval  Display prediction interval
(f)
Obtain the output for predicting at “Hardness = 700”.
In MTB11, use STAT > Regression > Predict
Response: ‘Abr.Loss’ , Enter individual values , Hardness = 700
Identify and label (highlight or circle by hand) the fitted value, ci and pi.