The following example was taken from Tamhane & Dunlop (2000, p. 441). It was slightly modified for the purposes of this assignment.

Are a person’s brain size and body size predictive of his/her intelligence? Data on the intelligence based on the performance IQ (PIQ) scores from the Wechsler Adult Intelligence Scale (revised), brain size based on the count from MRI scans (given as count/10,000), and body size measured by height in inches and weight in pounds on 38 college students are shown below.

The data is presented below. Use SPSS to help you answer the following questions.

Note: You may copy and paste the data in SPSS but make sure the data is entered correctly. Data entry errors automatically reduce you one letter grade (i.e., 10 points).

Performance IQ MRI Height Weight

124 81.69 64.5 118

150 103.84 73.3 143

128 96.54 68.8 172

134 95.15 65.0 147

110 92.88 69.0 146

131 99.13 64.5 138

98 85.43 66.0 175

84 90.49 66.3 134

147 95.55 68.8 172

124 83.39 64.5 118

128 107.95 70.0 151

124 92.41 69.0 155

147 85.65 70.5 155

90 87.89 66.0 146

96 86.54 68.0 135

120 85.22 68.5 127

102 94.51 73.5 178

84 80.80 66.3 136

74 93.00 74.0 148

86 88.91 70.0 180

84 90.59 76.5 186

134 79.06 62.0 122

128 95.50 68.0 132

102 83.18 63.0 114

131 93.55 72.0 171

84 79.86 68.0 140

110 106.25 77.0 187

72 79.35 63.0 106

124 86.67 66.5 159

132 85.78 62.5 127

137 94.96 67.0 191

110 99.70 75.5 192

86 88.00 69.0 181

81 83.43 66.5 143

128 94.81 66.5 153

124 94.94 70.5 144

94 89.40 64.5 139

89 93.59 75.5 179

Part I:

Let’s suppose you are interested in developing the simple linear least squares regression line to the data to determine if brain size is a statistically significant predictor for intelligence.

Assuming that all assumptions are tenable, conduct the analyses needed to determine if there are any outliers and influential points by considering the following statistics in your analyses: SDRESID, COOK’S D, and standardized DFBETA for the intercept and slope: Use the lower limit as the criteria for the appropriate statistics and use the .05 level of significance when appropriate. Take the first 3 places after the decimal – no rounding.

For SDRESID, if the df is NOT shown on the table, choose the df above and below that value. Then, choose the LARGER of the two values. For example, if the df is 47, select the values for 40 and 60 and then choose the larger of the two degrees of freedom.

In addition, on the SPSS data file for the outliers and influence statistics, evaluate each statistic considering the first 3 decimal places – no rounding (i.e., SDR_1 = .10789 = .107).

If any observations exceed the criteria, delete the observations by deleting the entire row. Show your work and report the observations that you deleted (i.e., observation 12):

Part II:

Re-run the regression analysis with the new data set in SPSS (with the observations that you identified in Part I deleted) and answer the following questions. Report (do not calculate unless asked) all information from SPSS – do not use any tables unless specifically asked (i.e., t* or F*-- report all answers from the output).

Note: Be sure to answer all parts to a question. For example, I will be looking for 4 responses for question #3. Please clearly label all answers for each verb – ex: decision: reject the null, report the 95% confidence interval: (54.5, 65.6), etc. If you do not clearly label each question with your answer, you will not receive full credit.

1. For your variables of interest, report descriptive statistics (i.e., mean, median, standard deviation, and sample size). Based on this statistical information, describe the shape of your distributions (i.e., approximately normally distributed, negative, or positive skew).
2. Report and interpret the correlation between the variables of interest (Analyze, Correlate, Bivariate).
3. Write the null and alternative hypotheses of no relationship between
   the two variables in the population (use correlation notation). Make a decision about the null hypothesis (reject or fail to reject), provide statistical evidence for your decision, and make a final conclusion within the context of this problem (i.e., begin your conclusion with ‘There is sufficient evidence (or insufficient evidence)… Always use this language for final conclusions).
4. Report the regression line that relates the two variables. Interpret the slope and intercept, if appropriate. If not appropriate, indicate so.
5. Report and interpret the appropriate effect size statistic.
6. Write the null and alternative hypotheses of no relationship between
   the two variables in the population (use regression notation). Make a decision about the null hypothesis, provide statistical evidence for your decision, and make a final conclusion within the context of this problem.
7. Report the 95% confidence interval for the population slope from SPSS. Interpret this interval within the context of this problem.
8. Calculate this interval by hand (you may take the statistics from the output and from the appropriate table to put in the equation for the confidence interval). Show your work.
9. Make a decision about your interval using the confidence interval results only . Provide statistical evidence for your decision, using the confidence interval results only . Make a final conclusion within the context of this problem.

Price: $30.88

Solution: The downloadable solution consists of 15 pages, 1588 words and 13 charts.
Deliverable: Word Document