Question 1:

Model Summary | Model | R | R Square | Adjusted R Square | Std. Error of the Estimate | 1 | .521a | .271 | .268 | 3.218 | a. Predictors: (Constant), Mother's height in inches, Father's height in inches | The model summary table indicates that R value is 0.521 which is a moderate correlation. The R square value 27% (R2) of the variation in son’s height is explained by the variation in the two independent variables “Father’s height in inches” and “Mother’s height in inches”. The adjusted R square value can be generalize to the population and indicates that 26.8% of the variation in son’s height is explained by the variation in father’s height and mother’s height which are predictor variables.

ANOVAa | Model | Sum of Squares | df | Mean Square | F | Sig. | 1 | Regression | 1531.552 | 2 | 765.776 | 73.954 | .000b | | Residual | 4110.845 | 397 | 10.355 | | | | Total | 5642.398 | 399 | | | | a. Dependent Variable: Son's Height in inches | b. Predictors: (Constant), Mother's height in inches, Father's height in inches |

The ANOVA table illustrates that the two predictor variables (Father’s height and Mother’s height) significantly predict son’s height (F2, 397= 73.954, p <0.001)

Coefficients | Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | 95.0% Confidence Interval for B | | B | Std. Error | Beta | | | Lower Bound | Upper Bound | 1 | (Constant) | 40.163 | 3.473 | | 11.563 | .000 | 33.335 | 46.992 | | Father's height in inches | .507 | .043 | .547 | 11.701 | .000 | .422 | .592 | | Mother's height in inches | -.089 | .054 | -.076 | -1.633 | .103 | -.196 | .018 | a. Dependent Variable: Son's Height in inches |

The Co efficient table shows the unstandardized coefficient, b, is 0.507 for the father’s height and (-0.089) for the mother’s height, which means the one unit increase in the Father’s height, the son’s height rises almost by 0.507. For one unit increase in Mother’s height, the son’s height decreased by 0.089. However, the standardized score is 0.547 which means for every one standard deviation increase in father’s height, the son’s height increases by 0.547 of a standard deviation. The t- value= 11.701 and is statistically significant (p<0.001). Although, b= 0.507, in the general population we would expect, with a 95% likelihood, that a true value of b would fall somewhere between 0.422 and 0.592. The strongest predictor based on the standardized beta value is the father’s height (0.547).
The mother’s height itself is not statistically significant (p= 0.103) and does not predict the son’s height.
Son’s height (y) = a + b1x1 + b2x2
Son’s height (y) = 40.163 + 0.507x1 - 0.089x

Question 2: A. By looking at the table, it is clear that the p-value for both the systolic and diastolic blood pressure is the same that is (p= 0.001), which means that according to the p-value, both of them are statistically significant. However, the chi-square value for systolic blood pressure (χ² = 141.4) is greater than the chi-square value for diastolic blood pressure (χ²= 80.2), which shows that the systolic blood pressure contributes more to the hypertension than the diastolic blood pressure. As far as comparison is concerned, since there are no standardized b-values, we cannot compare systolic and diastolic blood pressure. B. In order to estimate the effect of gender and current smoking on the predictability of hypertension, we need to calculate odds-ratio for both of these risk factors. Therefore, according to the odds ratio for gender [exp (B) = 0.776)], it is clear that the odds of hypertension are 0.776 times less for females compared to males (reference category), or in other words, females are 22.4% times less likely to develop hypertension than males. This is statistically significant with a p-value = 0.01. As far as current smoking is concerned, according to the odds-ratio [exp (B) = 1.386], it is evident that odds of hypertension are 1.386 times higher for current smokers than non-smokers and current smokers are 38.6% more likely to develop hypertension, assuming non-smokers as the reference category which is statistically significant with a p-value = 0.001.

C. Since male is the reference category, gender is a categorical variable. The coefficient refers to the comparisons of the odds at two different level of predictor. The b- value of the risk factor gender is -0.2524, and the corresponding odds-ratio is (exp (B) = 0.776) that means women are 22.4% less likely to develop hypertension compared to males. The p-value indicates that it is statistically significant (p= 0.01).