3. A study was conducted to relate birthweight (measured inhundreds of grams) and estriol level (measured in mg/24hr) in 11pregnant women. A simple linear regression model was fit to thesample data. Use the output from this page to answer the followingquestions.

   THE REG PROCEEDURE

ANALYSIS OF VARIANCE

   SOURCE DF SUM OF SQUARE MEAN SQUARE F-VALUE PR >F

MODEL 1 228.38    228.381 22.557 0.001045

   ERROR    9    91.12 10.124

TOTAL 10 319.5

  

   PARAMETER ESTIMATES

   Variable    DF    PARAMETERESTIMATE STANDARD ERROR    T-VALUE Pr > ltl

   Intercept 1 21.0123 2.4751    8.4891.5E-05

   estriol    1 0.6306    0.1328   4.749 0.00104

R-square    0.7148   

(a)10 Use the output above to fill in the following blanks totest whether there is a significant linear relationship betweenestriol level in pregnant women and birthweight:
We are interested in the hypotheses: H0 :___ vs HA :____ ,
where [define any parameters used above] ____
.
We can test this hypothesis using the test statistic ,
which follows a distribution with degrees of freedom if H0 istrue.
The p-value for this test is_____ .
So, at a significance level of ↵ =0 .05, we would (circleone):
accept the null hypothesis / reject the null hypothesis / fail toreject the null hypothesis
and conclude that [give your conclusion in the context of theproblem of interest and be as specific as possible about thedirection and magnitude of any effect]
.

(b)1 Based on above output, what birthweight would you expect for achild born to a mother with an estriol level of 15 mg/24hr?
(c)1 Construct a 95% Confidence Interval for the average birthweightat an estriol level of 15 mg/24hr. (Note that SE(E[Y]) =0.98).
(d)2 A 95% Prediction Interval corresponding to an estriol level of15 mg/24hr is (22.92, 38.02). Interpret this interval and contrastit with the interval found in (c).
(e)2 Can estriol be used to explain a large proportion of thevariability in birthweight? Justify your answer.
(f)2 Find Pearson’s correlation coefficient for this sample.Interpret this value.
(g)2 Will increasing a mother’s estriol level increase thebirthweight of her child? Justify your answer.

(h)4 Explain the assumptions underlying this regressionmodelling.
(i)4 Use the information from the next page to assess, as much aspossible, the suitability of this regression model.
(j)2 Based on all of these considerations, what can you concludeabout the relationship between birthweight and estriol level inpregnant women.