the ed. 11.2 General Concepts 459 TABLE 11.1 Sample data from the Greene-Touchstone study relating birthweight and estriol level in pregnant women near term Estriol Birthweight (mg/24 hr) (g/100) Estriol (mg/24 hr) Birthweight (g/100) X; Y₁ Xi Yi 2 12 7 25 17 17 32 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 EQUATION 11.2 DEFINITION 11.2 EXAMPLE 11.4 EXAMPLE 11.5 Source: Based on the American Journal of Obstetrics and Gynecology, 85(1), 1-9, 1963. Let's assume e follows a normal distribution, with mean 0 and variance o². The full linear-regression model then takes the following form: y = a+ẞx+e where e is normally distributed with mean 0 and variance σ². For any linear-regression equation of the form y=a+ẞx+e, y is called the depen- dent variable and x is called the independent variable because we are trying to predict y as a function of x. Obstetrics Birthweight is the dependent variable and estriol is the independent variable for the problem posed in Example 11.3 because estriol levels are being used to try to predict birthweight. One interpretation of the regression line is that for a woman with estriol level x, the corresponding birthweight will be normally distributed with mean a + ẞx and variance o². If σ2 were 0, then every point would fall exactly on the regression line, whereas the larger o² is, the more scatter occurs about the regression line. This rela- tionship is illustrated in Figure 11.2. How can ẞ be interpreted? If ẞ is greater than 0, then as x increases, the expected value of y = a + ẞx will increase. Obstetrics This situation appears to be the case in Figure 11.3a for birthweight (y) and estriol (x) because as estriol increases, the average birthweight correspondingly increases. If ẞ is less than 0, then as x increases, the expected value of y will decrease.

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The data shown below are the initial weights and gains in weight (in grams) of female rats on a high protein diet from 24 to 84 days of age. The point of interest in these data is whether the gain in weight is related to (dependent on) the initial weight. If so, then feeding experiments on female rats can be made more precise by adjusting for differences in initial weights of the rats. Statistically test this with a regression analysis.   Rat Number Initial Weight (gms) Weight Gain (gms) 1 50 128 2 64 159 3 76 158 4 64 119 5 74 133 6 60 112 7 69 96 8 68 126 9 56 132 10 48 118 11 57 107 12 59 106 13 46 82 14 45 103 15 65 104 I used excel's regression took pak and got the following:  SUMMARY OUTPUT                                 Regression Statistics               Multiple R 0.489416452               R Square 0.239528464               Adjusted R Square 0.181030653               Standard Error 8.869929833               Observations 15…

You do a survey where you ask people both their age and their income. You want to see if there is a relationship between these two variables, and you want to create an equation you can use to predict someone’s age from his/her income. What kind of hypothesis test or analysis should you do?a. One-Factor, Independent-Measures ANOVAb. Two-Factor ANOVAc. Correlation/Regressiond. Chi-Square Goodness of Fit