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Statistical Analysis and Regression: Exploring Correlations, Hypothesis Testing, and Data Interpretation

Solved assignment on regression analysis, hypothesis testing, and correlation interpretation.

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    Lane Chap. 14 2. The formula for a regression equation is Y’ = 2X + 9. a. What would be the predicted score for a person scoring 6 on X? The predicted score for that person would be, Y = 2*6+9 = 21 b. If someone’s predicted score was 14, what was this person’s score on X? In this case Y = 14 thus, 14 = 2X+9  X = (14 - 9)/2 = 2.5 Thus the score on X was 2.5. 6. For the X,Y data below, compute: a. r and determine if it is signi fi cantly different from zero. The obtained output from Minitab is given below, Correlation: X, Y Pearson correlation of X and Y = 0.849 P - Value = 0.032 From the above output we can see that the correlation coefficient be tween X and Y is 0.849 with corresponding P value 0.032. As the P value is smaller than the significance level of 0.05 so we can conclude that the correlation coefficient is significantly different from zero. b. the slope of the regression line and test if it differs signi fi cantly from zero. Using the data analysis tool pack of Excel the obtained output is given below, SUMMARY OUTPUT Regression Statistics Multiple R 0.8492 R Square 0.7211 Adjusted R Square 0.6514 Stand ard Error 3.5028 Observations 6

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    ANOVA df SS MS F Significance F Regression 1 126.9207 126.9207 10.3441 0.0324 Residual 4 49.0793 12.2698 Total 5 176 Coefficients Standard Error t Stat P - value Lower 95% Upper 95% Intercept 3.1231 3.1085 1.0047 0.3719 - 5.5075 11.7537 X 1.1332 0.3523 3.2162 0.0324 0.1550 2.1115 From the above output we can see that the slope of the regression line is 1.1332 with corresponding P value 0.0324. As the P value is smaller t han the significance level of 0.05 so we are rejecting the null hypothesis of insignificance and concluding that slope differs signi fi cantly from zero . c. the 95% con fi dence interval for the slope. The required 95% confidence interval for the slope is given in the above output which is (0.1550, 2.1115) X Y 4 6 3 7 5 12 11 17 10 9 14 21 Lane Chap. 17 5. At a school pep rally, a group of sophomore students organized a free raf fl e for prizes. They claim that they put the names of all of the students in the school in the basket and that they randomly drew 36 names out of this basket. Of the prize winners, 6 were freshmen, 14 were sophomores, 9 were juniors, and 7 were seniors. The results do not seem that random to you. You think it is a little fi shy that sophomores organized the raf fl e and also won the most prizes. Your school is composed of 30% freshmen, 25% sophomores, 25% juniors, and 20% seniors. a. What are the expected frequencies of winners from each class? The required expected frequencies of win ners from its class are,

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