Problem 1. To determine which students should receive scholarships ...

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Problem 1. To determine which students should receive scholarships university admis- sions officer decided tostudy the relationship between student's scorconthe SAT verbal est (taken the final yearofhighschool) and the student's college GPA at the endofthe sophomore year. Ten student records were examined with following results The reported exam scores are the actual scores divided 100. Student SAT GPA 4.8 2.4 6.6 3.5 3.8 3.0 2.8 10 3.2 Let be SAT score and be GPA. Then [x2 354.05 [r 93.14. [XY = 180.66. [x 58.5 and [Y 30.2. (1) Find the last squares regression linc. (2)Find the correlation coefficient r (3)Calculate the estimated standard crror in the linear regression. (4) Construct 99% confidence interval for the slope 8of the regression line (5) Predict student 's GPA at thc end of the sophomore year when his or her SAT verbal test scorci 5.5 (Usca90% prediction interval) (6) Do the data provide sufficient indicate that student SAT verbal test score provides mation to predict the student' GPA the end the sophomore year Test using .05. (a) Ho: H.: (b) statistic (c) Rejectic region (d) Conclusion 2 Study the association o with femoral necl bone density for moresmo cingtwins based data file Use Pack-years smoking predictor the Femoral neck bone density response variable. As described AB_ 02 S2018.pdf, Twin for less smoking twin. Twin2 for more smoking twin. Please review the data description the file BONEDEN.DOC. (1) Write the least square equation for the fitted regression line (2) is there association between femoral bonc density and smoking? Please test the slope of the linear regression. Find the p-value using JMP and make your choice. (3) What the difference in femoral neck bonc densities between participants who differ smoking by Please answer the question using the least square equation (4) What percent of variation femoral neck bone density explained by regression years? (5) What the standard deviation the estimated mean femoral neck bonc density 2 ycars old Australian, more smoking female twin who smoked 30 pack years? (You estimate the standard deviation estimated mean femoral neck bone density when : years page and 43 of the lecture notes You also choose use JMP find the tandard estimating average femoral bone density for more smoking female twin who smoked 30 pack years.) (6) Find the value of residual for the oldest Australian twin who smoked 20 pack years in wodifferent ways: a) using JMP (Red Triangle-> Save Columns-> Residuals): b) using the fitted cquation from the output (7) Estimate graphically 95% confidence interval for average femoral neel bone density for Australian female twins who smoked 20 pack years. (Red Triangle-> Save Columns- Mcan Confidence Interval) (8) would expect with 95% confidence that the mean femoral neck bone den- sity twin who smoked 20 pack years be between and

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