Elabies come in all shapes and sizes when they are born, so we are often interested in what variables may help determine a baby's birthweight. In Lab 8, we looked at the relationship between baby's birthweight and gestational peod, but now we also want to know if the baby's birthweight {in grams] is related to gestational period [in weeks}, height [in cm}, the mother's weight at the beginning of the pregnancy l[in kg}. and the mother's weight when the baby was born n kg}. We have the same random sample of rst-time mothers from Lab 3, with all the variables measured. Use the lvlinitab output. and the graphs provided on Moodle. to answer the following questions. Note that for Parts [a] through {m} [MDDDLE QUESTIONS 1 to 16}, you will use the part of the output labelled as Model 1 only. Regression Analysis: Birthweight versus GestPeriod, Height, Weightfirst, Weightfinal Regression Equation Birthweight = 1009 + 145.7 GestPeriod - 24.7 Height - 30.3 Weightfirst + 34.5 Weightfinal Coefficients Term Coel SE Coef T-Value P-Value Constant 1009 3263 0.31 0.759 GestPeriod 145.7 60.5 2.41 0.020 Height -24.7 15.6 -1.59 0.120 Weightfirst EDE 17.4 -1.74 0.089 Weightfinal 34.5 14.0 2.47 0.018 Model Summary S R-sq R-sqlad]) 494.855 22.87% 15.69% Analysis of Variance Source DF Adj 55 Adj MS F-Value P-Value Regression 4 3121892 7804 73 3.19 0.022 Error 43 10529908 Total 47 13651800 Fits and Diagnostics for Unusual Observations Obs Birthweight Fit Resid Std Resid 12 5220 3721 1499 3.21 R 45 4000 3653 347 0.91 X R Large residual X Unusual XResidual Plots for Birthweight Normal Probability Plot Versus Fits 90 1000 Residual Percent 10 -1090 1000 1000 3000 3300 3600 3900 4209 Residual Fitted Value Histogram Versus Order 1000 7.5 Residual Frequency -1000 -1000 -500 500 1000 1500 1 5 10 15 20 25 30 35 40 45 Residual Observation Order\fPART 3: INDIVIDUAL VARIABLES Since there was evidenoe of a relationship. we can look at the individual variables. Is there evidence that the average birthweight will increase 'when gestational period increases? State the hypotheses [Ho and Ha] in symbols. Which of the following is the correct interpretation of the parameter? Q a. Where B1 represents the increase in average [or mean or expected] birthweight when gestational period increases] with specified values for height] beginning weight] and end weightr for the population of all rsttime mothers. O b. Where B1 represents the increase in average [or mean or expected] birthweight when gestational period increases by 1 week, with specied values for height] beginning weightr and end weight, for the population of all rsttime mothers. 0 c. Where B1 represents the increase in average [or mean or expected] birthweight when gestational period increases by 1 week, with specied values for height, beginning weight, and end weight, for the population of all 48 rsttime mothers. 0 d. Where B1 represents the increase in average [or mean or expected] birthweight when gestational period. height, beginning weight, and end weight increases by 1 unit. for the population of all rst time mothers. State the value of the test statistic and pvalue from lvlinitab, adjusting the pvalue if necessary. Test statistic: F =|:| Briey asoees the strength of the evidence. State your conclusion in full context of the problem. Although the variable "GestPeriod" is significant, not all of the variables are. Which variable(s) would you consider removing from the model, and why? 7 A * B E E S's PAGiven that the 95% interval for the coefficient "GestPeriod" is (23.43, 267.97) grams, interpret this interval in the context of the problem. Note: although we have given you the interval here, make sure you know how to calculate it. It will not be on the Minitab Output. 1 B I IE Interpret the 95% prediction interval found on the Minitab output in the context of the problem. 1 A v B