MATH 325 DeVry Week 5 iLab

MATH 325 DeVry Week 5 iLab

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MATH 325 DeVry Week 5 iLab

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MATH 325 DeVry Week 5 iLab

 

MATH 325 DeVry Week 5 iLab

Using Minitab to Construct Linear Regression Models

The steps required for completing the deliverables for this assignment (screen shots that correspond to these instructions can be found immediately following them).Complete the questions below and paste the answers from Minitab below each question (type your answers to the questions where noted). Therefore, your response to the lab will be this ONE document submitted to the Dropbox.

Context (remember that statistics are far more than numbers or values – you need to know the context to perform a good analysis!).

Study: A nurse practitioner is studying the effect of blood sugar (glucose) control, which involves collecting the average daily AC and QHS (fasting) blood sugar levels of the patients to determine if there is relationship between these and the patients’ Hemoglobin A1C level. She hypothesizes that good blood sugar control will result in ideal Hemoglobin A1C levels and inadequate control of the patients’ blood sugar will result in high Hemoglobin A1C levels.

She also tracks other factors that may contribute to the patients’ control of their blood sugar such as carbohydrate intake, age, frequency of glucose checks, and insurance coverage of diabetic supplies. These will be analyzed in the next two labs.

Hemoglobin: Ideal Hemoglobin A1C levels are 6 to 7 whereas 8 or 9 merits concern and 10 and up are considered severely uncontrolled. Values less than 6 are rare in diabetic patients. However, levels lower than 6 can be found normally in patients that are not diabetic.

Blood Sugar: Glucose levels under 70 are considered low, between 70 and 110 is considered normal, 111 to 170 is considered moderately high, and values above 170 are considered high. There is some debate on the cut points, however, these are the values used to categorize glucose levels in this study.

Carbohydrates: Diabetic patients try to consume 14 servings of carbohydrates daily where each serving is approximately 15 grams. This study tracks the average grams of carbohydrates consumed on a daily basis by these patients.

View the Minitab tutorial on Linear Regression. The Linear Regression tutorial can be found by going to the Help menu in Minitab, selecting Tutorials then selecting Regression. Read through Uses, Data and How To in the Tutorial window.

Any mention of the F statistic and ANOVA may be ignored. ANOVA will be discussed in much more detail in the next lab and we will expand on it then.

Note: The data files referenced in the tutorial are available in DocSharingfile (Minitab_Sample DataSets_HelpMenu). I suggest you print out the steps needed to perform the deliverables for the lab and as these items/steps come up in the tutorials, also use the HealthCareData.mpj data set to work along at that point.

Scatter Plot

To obtain a simple scatter plot using Minitab:

One of the first steps in the analysis of the study data is to create a scatter plot that compares the quantitative variables. Create each of the following scatter plots, find Pearson’s correlation coefficient, and perform the corresponding linear regression analysis in each case. Detailed instructions follow on the next page.

Create a scatter plot, find the r value, and perform the regression analysis that compares the patients’ average daily blood sugar level to their Hemoglobin A1C level.

Create a scatter plot, find the r value, and perform the regression analysis that compares the patients’ carbohydrate intake to average glucose levels.

Create a scatter plot, find the r value, and perform the regression analysis that compares the patients’ carbohydrate intake to Hemoglobin A1C levels.

To Obtain a Sample Scatter Plot Using Minitab

  1. Open the HealthCareData.mpj file using Minitab.
  2. From the menus, select Graph, Scatterplot
  3. Choose Simple and then click OK.
  4. Select the following variable pairs for the scatter plots
    1. y-variables: Hemoglobin x-variables: Glucose
    2. y-variables: Glucose x-variables: carb_intake
    3. y-variables: Hemoglobin x-variables: carb_intake
  5. Generate all three scatter plots by clicking OK and examine the results. Copy and paste each graph below. To Obtain Linear Regression Using Minitab
  6. From the menus, select Stat, Regression and then General Regression
  7. Select the following variable pairs for the regression analysis (you will need to do this 3 separate times). Response = y-axis andModel = x-axis
    1. Response: Hemoglobin Model: Glucose
    2. Response: Glucose Model: carb_intake
    3. Response: Hemoglobin Model: carb_intake
  8. Then click Graphs, select Standardized and select Histogram and Normal probability plot and click OK.
  9. Click OK in the Linear Regression window to perform the analysis.
  10. Think about it: Were there any strong relationships indicated? Were there any extreme values that might skew results? How would you use the regression equations generated by the software? What preliminary conclusions would be supported and what further study indicated?
  11. Deliverable: Save this document and submit it as Week_5_i-Lab_YourNameHere.docx to the Dropbox.

Linear Regression

Linear Regression estimates the coefficients of the linear equation, involving one or more independent variables that best predict the value of the dependent variable. For example, you can try to predict a salesperson’s total yearly sales (the dependent variable) from independent variables such as age, education and years of experience.

Example. Is the number of games won by a basketball team in a season related to the average number of points the team scores per game? A scatter plot indicates that these variables are linearly related. The number of games won and the average number of points scored by the opponent are also linearly related. These variables have a negative relationship. As the number of games won increases, the average number of points scored by the opponent decreases. With linear regression, you can model the relationship of these variables. A good model can be used to predict how many games teams will win.

Statistics. For each variable: number of valid cases, mean, and standard deviation. For each model: regression coefficients, correlation matrix, part and partial correlations, multiple R, R2, adjusted R2, change in R2, standard error of the estimate, analysis-of-variance table, predicted values, and residuals. Also, 95%-confidence intervals for each regression coefficient, variance-covariance matrix, variance inflation factor, tolerance, Durbin-Watson test, distance measures (Mahalanobis, Cook, and leverage values), DfBeta, DfFit, prediction intervals, and case-wise diagnostics. Plots: scatter plots, partial plots, histograms, and normal probability plots.

For the purpose of testing hypotheses about the values of model parameters, the linear regression model also assumes the following:

  1. The error term has a normal distribution with a mean of 0.
  2. The variance of the error term is constant across cases and independent of the variables in the model. An error term with non-constant variance is said to be heteroscedastic.
  3. The value of the error term for a given case is independent of the values of the variables in the model and of the values of the error term for other cases.