Question: Greene and Touchstone conducted a study to relate birth weight and Estriol level in pregnant women as given in the table below:
i | Estriol (mg/24hr) Xi | Birthweight (g/100) Yi | i | Estriol (mg/24hr) Xi | Birthweight (g/100) Yi | 1 | 7 | 25 | 17 | 17 | 32 | 2 | 9 | 25 | 18 | 25 | 32 | 3 | 9 | 25 | 19 | 27 | 34 | 4 | 12 | 27 | 20 | 15 | 34 | 5 | 14 | 27 | 21 | 15 | 34 | 6 | 16 | 27 | 22 | 15 | 35 | 7 | 16 | 24 | 23 | 16 | 35 | 8 | 14 | 30 | 24 | 19 | 34 | 9 | 16 | 30 | 25 | 18 | 35 | 10 | 16 | 31 | 26 | 17 | 36 | 11 | 17 | 30 | 27 | 18 | 37 | 12 | 19 | 31 | 28 | 20 | 38 | 13 | 21 | 30 | 29 | 22 | 40 | 14 | 24 | 28 | 30 | 25 | 39 | 15 | 15 | 32 | 31 | 24 | 43 | 16 | 16 | 32 | | | |
1. Compute the slope and intercept of the estimated regression line based on above table. 2. If low birthweight is defined as <span id="MathJax-Element-1-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="≤" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 16.8px; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">≤≤2500 g, for what estriol level would the predicted birth weight be 2500 g? 3. What is the predicted birth weight if a pregnant woman has an estriol level of 15 mg/24hr? 4. Fit a linear regression model based on the data using R. 5. Test for the significance of the regression line derived for the birthweight - estriol data.
Linear RegressionLinear Regression is a method of modeling a dependent variable as a linear function of independent variables. When the number of independent variables is single, it is called Simple Linear Regression. Using the regression models, the unknown values of the dependent variable can be predicted using the known values of the independent variable.
Answer and Explanation:Since the answer to the question requires a lot of computation, we can either use a calculator or the R statistical software application. 1. Slope and Intercept of the regression lineLet the regression line be<span id="MathJax-Element-2-Frame" class="mjx-chtml MathJax_CHTML" tabindex="0" data-mathml="Y=mX+b" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; font-size: 16.8px; overflow-wrap: normal; word-spacing: normal; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding-top: 1px; padding-bottom: 1px; position: relative;">Y=mX+bY=mX+b
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