Question

The INTERSALT Study investigators collected standardized data on timed 24-hour urinary excretion for 10,079 men and women from 52 population samples in 32 countries (Brown et al.) [14] One of the goals of the INTERSALT Study was to quantify the relationship between 24-hour urinary Na (y) and estimated 24-hour urinary Na (x) obtained from casual urine specimens at one point in time. The investigators presented a simple linear regression of y on x, separately for men and women. The regression equation for men was:

Y = 1.03 x − 7.19, with R² = 0.27, n = 1369

1. What does the R² of 0.27 mean in words?

2. What is a two-sided p-value for the regression? (Hint: Assume that a t distribution with > 200 df is the same as a N(0,1) distribution.)

3. What is the estimated standard error of the slope estimate? (Hint: Use the t test for simple linear regression.)

4. Provide a 95% Cl for the true slope (β).

Answer 1

1)

R2 = 0.27 means that our model (1.03x - 7.19) explains 27% variability in 24 hour Urine Na due to Casual Urine in one point of time.

2)

For casual potassium, test statistic is:

Since sample size is very large, we can use normal distribution for p-value.

4)

For 95% confidence interval, (Since sample size is very large)

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