Question

Be sure to clearly state the hypotheses in the hypothesis tests and state the conclusions in terms of the problem. Use ?=.?? for all tests.

The following table presents shear strength (in kN/mm) and weld diameters (in mm) for a sample of spot welds.

Diameter Strength

4.2                51

4.4                54

4.6               69

4.8                81

5.0                75

5.2               79

5.4                89

5.6               101

5.8                98

6.0               102

1.Construct a scatterplot of strength (y) versus diameter (x). Does it appear as though a linear model is appropriate? Explain.

2.Compute the correlation coefficient between x and y.

3.Compute the least-squares line for predicting shear strength from weld diameter.

4.Compute the fitted value and residual for each point. (This can be done with a simple option selection in Minitab.

5.Predict the strength for a diameter of 5.5 mm.

6.Can the least-squares line be used to predict the strength for a diameter of 8 mm? If so, predict the strength. If not, explain why not.

7.For what diameter would you predict a strength of 95 kN/mm?

8.Compute the coefficient of determination and explain what it represents.

9.Compute a 90% confidence interval for the mean shear strength of welds with diameters of 5.1 mm.

10.Compute a 99% prediction interval for the shear strength of particular weld with diameter 5.1 mm.

11.Construct two residual plots (residuals versus the fitted y values and a normal probability plot of the residuals) and discuss what they tell you about the fit of the model and whether the model assumptions are satisfied.

Please solve using Minitab and show step

Answer 1

Using Minitab:

Click Stat > Regression > Regression... on the top menu, as shown below:

You will be presented with the following Regression dialogue box:

Click the OK button. The output that Minitab produces is shown below.

1.Construct a scatterplot of strength (y) versus diameter (x). Does it appear as though a linear model is appropriate? Explain.

R squared value is 92.3 % which very strong. so we can say  linear model is more appropriate.

2.Compute the correlation coefficient between x and y.

Correlation: Diameter, Strength

Pearson correlation of Diameter and Strength = 0.961

3.Compute the least-squares line for predicting shear strength from weld diameter.

From the above minitab output:

The regression equation is
Strength = - 67.69 + 28.94 Diameter

4.Compute the fitted value and residual for each point. (This can be done with a simple option selection in Minitab.

5.Predict the strength for a diameter of 5.5 mm.

The regression equation is
Strength = - 67.69 + 28.94 * 5.5

=91.47 approximately 92

Post remaining questions separately.

Hope this will be helpful. Thanks and God Bless.