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### 14.8 Problems

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Describe a process in operations or production where a simple linear regression would be an applicable model.

Identify the independent (X) and dependent (Y) variables.

Sketch the relationship between X and Y.

Give an interpretation of the slope for this situation.

How could this regression model be used in this situation?

Maplecreek Estates is offering custom-built homes for sale in a suburban location. To date, homes have been built on 10 of the 25 available lots. The file MaplecreekEstatesjmp contains the lot number, house size (measured in square feet), and house price. Use this data to construct a simple linear regression to predict house price based on house size.

Use JMP to perform the analysis and show the Summary of Fit and Parameter Estimates tables. Plot the data with the least squares regression line and show the 95% confidence and prediction intervals on the plot. Use the JMP annotate tool to identify the confidence and prediction intervals.

State the regression equation. Interpret the meaning of the slope and intercept. What is the importance of the p-value of the associated t-Ratio?

Justify whether the house price versus house size is a good or poor fit in as many ways as you can.

Give an interpretation of R

^{2}.Estimate the average house price for a 3000 sq. ft. home and a 3800 sq. ft. home. Which is the more precise estimate? Why? Discuss reservations you might have in using the regression model to make these predictions.

Construct residual plots to verify the regression assumptions. How well are the assumptions satisfied?

A retail grocer is considering running a one-day special on five-pound bags of white sugar. Prior to setting the sale prices, the grocer analyzes past data on sugar sales. The data are contained in the file sugar_sales.jmp. Price is given in cents and sales in number of units sold per day.

Estimate the regression equation.

Is this linear regression an adequate model for the data? What objective evidence can you cite to justify your answer?

The grocer is considering sale prices of $1.35 or $1.49. What sales could he expect at each of these prices? Discuss any reservations to these predictions.

Find and interpret a 95% confidence interval for mean sales for a price of $1.35.

Find and interpret a 95% prediction interval on sales for a price of $1.35.

Which interval would be of most use to the grocer in this situation? Explain your choice.

The data file electronic component jmp contains cost data for various batch sizes of a manufactured electronic component. Use the data to develop a regression model that relates cost and batch size.

State the regression equation.

Assess the quality of the model.

Give a statistical interpretation of the intercept estimate.

Give a business interpretation of the intercept estimate.

Give a statistical interpretation of the slope estimate.

Give a business interpretation of the slope estimate.

The data file fasteners.jmp contains cost data for the production of batches of fasteners used in the assembly of cellular telephone relay towers.

Using JMP, perform a simple regression analysis where cost is the dependent variable (Y) and batch size is the independent variable (X). Give the regression equation. Give an interpretation of the slope estimate. Is the slope estimate significant?

Assess the goodness-of-fit of this model. Discuss any patterns apparent in the residual plot.

Discuss possible business reasons for the inadequacy of the model.

An official at the Winston Downs Racetrack would like to develop a model to forecast the amount of money bet (in millions of dollars) based on attendance (in thousands). A random sample of 15 days is selected, with the results given in the file betting_attendance.jmp.

Develop a forecasting model using simple regression that could be applied in this situation. Give the regression equation.

Assess the goodness-of-fit of this model.

Note on the residual plot and the X-Y data plot the point that appears to be an outlier. Examine the influence of this point on the regression estimates by excluding that point in the JMP table and refitting the model.

Compare the differences between the two regression models. Compare the predicted amount of money bet with an attendance of 35,000 from the two models.

Discuss what actions should be taken to determine whether this data point should be retained for the purposes of model fitting and prediction.

Data collected on cross-selling from a bank were used to estimate a simple linear regression model relating the number of households at each branch who use internet banking to the average number of products sold at that branch. The R

^{2}was found to be 0.16 and the slope estimate was significant (p-value < 0.0001). There were no apparent patterns in the residual plot. The data are contained in the file cross_selling.jmp.Verify that these measures of model adequacy are correct.

Give possible reasons for the seemingly low R

^{2}. Suggest possible actions to achieve a better model.