DATA ANALYSIS
Q1. WHICH OF THE ABOVE VARIABLES ARE SIGNIFICANTLY BIVARIATELY ASSOCIATED RELATED TO BMI?
Hint: Run a bivariate correlation analysis (be sure to request significance values). Paste the syntax below. Don’t worry about the output yet, we’ll get to that in a bit.
Q2. REPORT THE CORRELATION COEFFICIENT AND P VALUE BETWEEN BMI AND EACH OF THE FOLLOWING VARIABLES (ROUND TO THREE DECIMAL PLACES):
LDL:
Glucose:
Age:
Q3. GIVEN BMI AS THE OUTCOME VARIABLE, WHICH PREDICTOR HAS THE STRONGEST RELATIONSHIP WITH BMI?
Q4. REPORT THE PERCENT OF VARIANCE (R2) IN BMI EXPLAINED BY THE PREDICTOR WITH THE STRONGEST BIVARIATE RELATIONSHIP.
Report as a percent and round to two decimal points.
Q5. SET UP A REGRESSION BETWEEN BMI (AS THE OUTCOME) AND TWO PREDICTORS: LDL, AGE.
Create a Publication ready regression table that contains at least the following items:
• Regression coefficient and confidence intervals for predictors
• P value for all predictors
• Overall model fit
• Number of observations
Note: Do NOT simply cut and paste Stata output. No journal would ever accept that for publication. Your regression table has to be well formatted.
Hint: You might remember the asdoc command? Round to three decimal places for all values (yes, this means a little clean up of the word doc!). For overall fit, report F, R2 and P value
Q6. INTERPRET THE RESULTS NARRATIVELY.
Hint: Interpret at both the overall model level (e.g., F, R2 and P value) and coefficient level (e.g., coefficient and confidence intervals and p-values). Interpret the difference in BMI for a ten unit change in LDL and ten-year change in age.
Q7. NOW ADD GLUCOSE TO THE MODEL AND RUN THE MULTIPLE REGRESSION AGAIN.
What difference do you see in the model fit? Report F, R2 and P value and compare it with the previous model. How do these two models (with and without glucose) differ?
Q8. NOW NARRATIVELY INTERPRET THE EFFECT OF THE COEFFICIENTS IN THE NEW MODEL AND IN A SEPARATE SENTENCE COMMENT ON HOW EFFECTS CHANGED RELATIVE TO THE ORIGINAL MODEL WITHOUT GLUCOSE.
As before, interpret changes in BMI as a function of a ten unit change in each coefficient.
Q9. WHAT DOES THE RELATIVELY LOW R2 VALUE OF THE FULLY ADJUSTED MODEL TELL US?
Q10. WHICH ONE OF THESE STATEMENTS IS CORRECT?
• Regression coefficients and fitted values represent means.
• R-squared and prediction intervals represent variability.
• We interpret the coefficients for significant variables the same way regardless of the R-squared value.
Q11. THOUGHT PROBLEM: WE ARE GOING TO COMPARE A COUPLE OF MADE UP (BUT PLAUSIBLE) MODELS. BUT SOMETHING ODD IS GOING ON. WHAT MIGHT IT BE?
Below, you see an output from a regression between z (dependent variable) and 9 independent variables (y1, y2, …y9). The output shows that there is a highly significant F statistic (p=0.003) and 50% of the variance in z is explained by the combination of predictors—but none of the independent variables is significant!!
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