# 1 conduct a multiple linear regression using spss

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1. Conduct a multiple linear regression using SPSS. Provide relevant SPSS output and assess the statistical significance of the effect of sex, age, and BMI on systolic blood pressure. (10 points) Tests of Between-Subjects Effects Dependent Variable: Systolic Blood Pressure Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 34695.918 a 3 11565.306 26.249 .000 Intercept 24438.019 1 24438.019 55.466 .000 age 10524.126 1 10524.126 23.886 .000 bmi 10856.756 1 10856.756 24.641 .000 sex 12286.078 1 12286.078 27.885 .000 Error 174476.082 396 440.596 Total 7010836.000 400 Corrected Total 209172.000 399 a. R Squared = .166 (Adjusted R Squared = .160) Parameter Estimates Dependent Variable: Systolic Blood Pressure Parameter B t Sig. 95% Confidence Interval

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Std. Error Lower Bound Upper Bound Intercept 59.621 8.907 6.694 .000 42.110 77.133 age .629 .129 4.887 .000 .376 .882 bmi 1.434 .289 4.964 .000 .866 2.002 [sex=1] 11.372 2.154 5.281 .000 7.138 15.606 [sex=2] 0 a . . . . . a. This parameter is set to zero because it is redundant. 2. Explain the assumptions of Linearity, Sampling independence, Normality, and Homoscedasticity (or equal variance). How would you test whether these have been met? (Note: for the exam you do not need to test these assumptions) (5 points) For linearity assumption to be met in linear regression, there should be linear relationship between the dependent variable and each of the independent variables that are continuous variables. This assumption can be tested using Pearson correlation. The assumption of sample independence is that each case/respondent must be selected independent of every other case/respondent so that the chance of selecting a particular case/respondent does not in any way influence the chance of selecting another case/respondent. To ensure that this assumption is met, the researcher must carefully design the sampling protocol. The assumption of normality requires that the dependent variable is normally distributed and that the continuous independent variables are also normally distributed. This assumption can
be tested using either Kolmogorov-Smirnova’s Test and Shapiro-Wilk’s Test of Equality of normality. The assumption of homoscedasticity (or equal variance) requires that the error variance remains stable/equal throughout the various values of the dependent variable. This assumption can be tested by assessing the distribution of the regression residuals, and more analytically by using the Breusch–Pagan test. 3. Explain the practical implications of your finding. Include a reference to the R square of the model in your discussion. (5 points) The fitted logistic regression model has an R-square of 0.166. This means that the variations in the independent variables are able to explain 16.6 % of all the variations in the dependent variable. This is reasonable as there are many other factors (other than age, BMI, and gender) that can affect systolic blood pressure (which is the dependent variable in this exercise). In other words, if this model were to be used in practical settings, one must know that it is only capable of accounting for 16.6% of the variations/changes in the systolic blood pressure.

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