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

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Lane Chap. 142. 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 = 21b. 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 = 2.5Thus the score on X was 2.5.6. For the X,Y data below, compute:a. r and determine if it is significantly different from zero.The obtained output from Minitab is given below,Correlation: X, YPearsoncorrelationofXandY=0.849P-Value=0.032From the above output we can see that the correlation coefficient between X and Y is 0.849 withcorresponding P value 0.032. As the P value is smaller than the significance level of 0.05 so we canconclude that the correlation coefficient is significantly different from zero.b. the slope of the regression line and test if it differs significantly from zero.Using the data analysis tool pack of Excel the obtained output is given below,SUMMARYOUTPUTRegression StatisticsMultiple R0.8492R Square0.7211Adjusted R Square0.6514Standard Error3.5028Observations6

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ANOVAdfSSMSFSignificanceFRegression1126.9207126.920710.34410.0324Residual449.079312.2698Total5176CoefficientsStandard Errort StatP-valueLower 95%Upper95%Intercept3.12313.10851.00470.3719-5.507511.7537X1.13320.35233.21620.03240.15502.1115From the above output we can see that the slope of the regression line is 1.1332 with corresponding Pvalue 0.0324. As the P value is smaller than the significance level of 0.05 so we are rejecting the nullhypothesis of insignificance and concluding that slopediffers significantly from zero.c. the 95% confidence interval for the slope.The required 95% confidence interval for the slope is givenin the above output which is (0.1550, 2.1115)XY463751211171091421Lane Chap. 175. At a school pep rally, a group of sophomore students organized a free raffle for prizes. They claim thatthey put the names of all of the students in the school in the basket and that they randomly drew 36names 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 littlefishy thatsophomores organized the raffle 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 winners from its class are,

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