The following table presents shear strengths (in kN/mm)

Chapter 7, Problem 8E

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QUESTION:

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

a. Construct a scatterplot of strength (y) versus diameter (x). Verify that a linear model is appropriate.

b. Compute the least-squares line for predicting strength from diameter.

c. Compute the fitted value and the residual for each point.

d. If the diameter is increased by 0.3 mm, by how much would you predict the strength to increase or decrease?

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

f. 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.

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

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Questions & Answers

QUESTION:

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

a. Construct a scatterplot of strength (y) versus diameter (x). Verify that a linear model is appropriate.

b. Compute the least-squares line for predicting strength from diameter.

c. Compute the fitted value and the residual for each point.

d. If the diameter is increased by 0.3 mm, by how much would you predict the strength to increase or decrease?

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

f. 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.

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

ANSWER:

Step 1 of 9

a.

To construct the scatterplot of the given data that is Strength vs Diameter;

The scatterplot is illustrated by plotting the diameter on the x-axis and strength on the y-axis.

 

                                             

 

Since the data points are approximately linearly plotted, it can be said that there is almost a linear relationship between the variables.

Therefore, there is a positive linear relationship between strength and diameter.

 

 

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