国外大学SPSS经典教程

国外大学SPSS经典教程

EXERCISES - ACADEMIC YEAR 2013 - 2014

MATHEMATICAL TECHNIQUES

To improve its defense system against incoming intercontinental ballistic missiles, the United States has been developing a new type of Ground Based Interceptor or GBI (Figure 1). Over the past years, the new type of interceptor has been tested intensively at the Vandenberg Air Force base, California.

Figure 1. Launch of a Ground Based Interceptor (GBI)

One of the tests consisted of monitoring the elapse of time and the distance traveled between the launch stage and the self-destruction of the test missiles. The test results are partially shown in Table 1. The full dataset can be found in Math tech_dataset.xlsx.

Table 1. Partial Dataset

Time [s] Distance [km]

5.85 1.09

5.99

… 83.85 0.85 82.30 …

Question 1

Perform a linear regression analysis for the given dataset. Does a linear model sufficiently explain the relation between Time and Distance? Evaluate this based on the calculated correlation coefficient. Is the linear regression model significant? Determine confidence intervals for the parameters of the linear model. Generate a scatter plot as well. Visualize the confidence intervals for the regression line and the individual values in the scatter plot.

国外大学SPSS经典教程

Question 2

Is there a non-linear trend present in the data? Evaluate this visually by plotting both the standardized and unstandardised residuals as a function of Time. Which type of model would probably be more suitable? Visualize the corresponding confidence intervals for the regression line and the individual values.

Question 3

Generate a new variable that corresponds with Time². Perform a multi-linear regression analysis with Time and Time² as independent variables. Determine the regression factors for this model. Which factors are significant? Determine the confidence intervals for each factor. Perform another multi-linear regression analysis. Only now assume that the constant factor equals zero. Discuss the differences with the previous analysis.

Question 4

Evaluate the normality of the unstandardized residuals for the model without constant factor as obtained in Question 3 while using Shapiro-Wilk. Interpret the obtained Q-Q plots. Perform another visual normality check by plotting the histogram for the unstandardized residuals and the normal distrubtion curve on top of each other.

Question 5

Use non-linear regression analysis instead of multi-linear regression analysis to evaluate the suitability of a quadratic model without constant factor. Estimate the regression factors. Compare with the model that was obtained while using multi-linear regression analysis (Question 3).

Good Luck!!!

Date of submission: January 23th, 2014 (the day of the exam)

Format: A full individual report in which the necessary SPSS output is included and discussed in detail. Please provide a clear answer to each question. Always include a definition of the test hypotheses and significance levels applied. If possible, disccuss how part of the SPSS output could be calculated manually. Generate and interpret the required visual output (graphs,…). Hand in a printed version of this report (max. 15 pages!) on the day of the exam.

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