Reference no: EM133732619

Assignment: Null & Alternative Hypothesis

For all problem write out the null hypothesis and alternative hypothesis. State α as appropriate.

I. We want to examine the relationship between body temperature Y and heart rate X. Further, we would like to use heart rate to predict the body temperature.

1. Use the "BodyTemperature.txt" data set to build a simple linear regression model for body temperature using heart rate as the predictor.

2. Interpret the estimate of regression coefficient and examine its statistical significance.

3. Find the 95% confidence interval for the regression coefficient.

4. Find the value of R2 and show that it is equal to sample correlation coefficient.

5. If someone's heart rate is 75, what would be your estimate of this person's body temperature?

II. We believe that gender might also be related to body temperature and could helpus to predict its unknown values.

1. Use the "BodyTemperature.txt" data set to build a multiple linear regressionmodel for body temperature using heart rate and gender as predictors

2. How much R2 did increase compared the above simple linear regressionmodel?

3. Explain the estimates of regression coefficients in plain language.

4. Find the 95% confidence intervals for regression coefficients.

5. If a woman's heart rate is 75, what would be your estimate of her body temperature?What would be your estimate of body temperature for a man whoseheart rate is 75.

III. We would like to predict a baby's birthweight (bwt) before she is born using hermother's weight at last menstrual period (lwt).

1. Use the birthwt data set to build a simple linear regression model, wherebwt is the response variable and lwt is the predictor.

2. Interpret your estimate of regression coefficient and examine its statisticalsignificance.

3. Find the 95% confidence interval for the regression coefficient.

4. If mother's weight at last menstrual period is 170 pounds, what would beyour estimate for the birthweight of her baby?

IV. For the above problem, use both mother's weight at last menstrual period (lwt)and her smoking status (smoke) to predict birthweight.

1. Interpret the estimates of regression coefficients and comment on their statisticalsignificance.

2. Find the 95% confidence interval for regression coefficients.

3. If mother's weight at last menstrual period is 170 pounds and she was smoking during her pregnancy, what would be your estimate for the birthweight of her baby?

V. We want to predict percent body fat using the measurement for neck circumference.

1. Use the bodyfat data set to build a simple linear regression model forpercent body fat (siri), where neck circumference (neck) is the predictor.In this data set, neck is measured in centimeters.

2. What is the expected (mean) increase in the percent body fat correspondingto one unit increase in neck circumference.

3. Create a new variable, neck.in, whose values are neck circumference ininches. Rebuild the regression model for percent body fat using neck.inas the predictor.

4. What is the expected (mean) increase in the percent body fat for one unit (1 inch = 2.54 centimeter) increase in neck.in.

5. Compare the estimates of regression coefficient tobs values and R2 values between the two models.