Question: The plot below is a two way scatter plot of head circumference (cm) vs gestational age (weeks) for a sample of 100 low birthweight infants, and the output from fitting a simple linear regression model to the data, regressing headcirc (Y) on gestage(X).

Analysis of Variance

Sum of Mean

Source DF Squares Square F Value Pr > F

Model 1 386.86737 386.86737 152.95 <.0001

Error 98 247.88263 2.52941

Corrected Total 99 634.75000

Root MSE 1.59041 R-Square 0.6095

Parameter Estimates

Parameter Standard

Variable Label DF Estimate Error t Value Pr > |t|

Intercept Intercept 1 3.91426 1.82915 2.14 0.0348

gestage gestage 1 0.78005 0.06307 12.37 <.0001

 Give the least squares regression line estimated from the data?

 Interpret the regression coefficient representing the relationship between gestational age and head circumference.

 Test the null hypothesis that the true slope relating head circumference to gestational age is zero using a two-sided test at the 0.05 level of significance. State the null and alternative hypothesis, and give the appropriate test statistic, the distribution the test statistic (with appropriate degrees of freedom) and conclusion. Interpret result.

 Estimate and provide a 95% confidence interval for the slope describing the relationship between head circumference and gestational age

 Estimate and provide a 95% confidence interval for the expected (mean) head circumference corresponding to a gestational age of 29 weeks. You will need to know that the standard error of the estimated mean head circumference at 29 weeks is 0.159cm.

 Suppose that a new newborn is selected from the underlying population of low birthweight infants with gestational age of 29 weeks. Give a 95% prediction interval for the new value of head circumference.

 Explain the difference between a prediction interval and a confidence interval.

 Given that n = 30, S2Y|X = 9, and SSY = 356, fill out the following analysis of variance table for a regression.

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