Question

A study conducted at Baystate Medical Center in Springfield, Massachusetts, identified factors that affect the risk of giving birth to a low-birth-weight baby. Low birth weight is defined as weighing fewer than 2,500 grams (5 pounds, 8 ounces) at birth. Low-birth-weight babies have increased risk of health problems, disability, and death. [Source: Hosmer, D., & Lemeshow, S. (2000). Applied logistic regression (2nd ed.). Hoboken, NJ: Wiley.] Suppose that you conduct a similar study focusing on the age, prepregnancy weight, and weight gain of the mothers as predictors of their babies’ birth weight among 50 low-birth-weight babies. You use a statistical software package to run a multiple regression predicting birth weight in grams (BIRTHWT) from the mother’s age in years (AGE), the mother’s prepregnancy weight in pounds (MOMWT), and the mother’s weight gain in pounds (GAIN). Use the output that follows to answer the following questions. Correlations BIRTHWT AGE MOMWT GAIN BIRTHWT Pearson Correlation 1.000 -0.4189 -0.1500 0.2174 Sig. (two-tailed) 0.0025 0.2985 0.1293 N 50 50 50 50 AGE Pearson Correlation -0.4189 1.000 0.1465 -0.1129 Sig. (two-tailed) 0.0025 0.3099 0.4350 N 50 50 50 50 MOMWT Pearson Correlation -0.1500 0.1465 1.000 -0.1925 Sig. (two-tailed) 0.2985 0.3099 0.1804 N 50 50 50 50 GAIN Pearson Correlation 0.2174 -0.1129 -0.1925 1.000 Sig. (two-tailed) 0.1293 0.4350 0.1804 N 50 50 50 50 Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 0.457ª 0.208 0.157 360.352 a. Predictors (constant): AGE, MOMWT, GAIN ANOVA b Model Sum of Squares df Mean Square F Two-Tailed Sig. 1 Regression 1572579.1 3 524193.0 4.037 0.0125ª Residual 5973256.5 46 129853.4 Total 7545835.6 49 a. Predictors (constant): AGE, MOMWT, GAIN b. Dependent Variable: BIRTHWT Coefficientsª Model Unstandardized Coefficients Standardized Coefficients t Two-Tailed Sig. B Std. Error Beta 1 (Constant) 2790.6659 377.4385 7.3937 0.0000 AGE –32.2993 10.9774 -0.3917 -2.9423 0.0051 MOMWT –0.8902 1.9502 -0.0615 -0.4564 0.6502 GAIN 5.6847 4.7271 0.1614 1.2026 0.2353 a. Dependent Variable: BIRTHWT The estimated regression equation is: Ŷ = AGE + MOMWT + GAIN + Following is part of a write-up of your results. Using the information in the table just given, fill in the blanks with the appropriate words or phrases that correctly describe the results of your study. Assume that you have nondirectional null hypotheses and are using a significance level of 0.05. Multiple regression was used to determine whether low-birth-weight babies’ birth weights could be predicted from their mothers’ ages, prepregnancy weights, and weight gain over the course of the pregnancy. The overall regression was [F(3, 46) = , p = , and R² = ]. Only was a significant predictor of birth weight (t = , p = ). Suppose that the coefficients of all of the predictor variables you included in the regression model were significantly different from zero (that is, all three are significant). Which of the following comparisons might best help you think about which variable is the most important predictor? Comparing the significance levels of the coefficients Comparing the magnitudes of the standard errors of the coefficients Comparing the magnitudes of the beta values (the standardized coefficients) Comparing the magnitudes of the B values (the unstandardized coefficients)

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