Question

IV. Your friend mentions that pre-test measures was taken and wants to take that information into account. You suggest using the pre-test value as a covariate to see what effect does it have on the response. First you fit a simple linear regression of diastolic on pre-diastolic.

Call:

lm(formula = diastolic ~ prediastolic, data = a)

Residuals:

    Min      1Q Median      3Q     Max

-11.268 -4.627   1.101   3.652 10.644

Coefficients:

             Estimate Std. Error t value Pr(>|t|)   

(Intercept)   30.7307     9.9041   3.103 0.00485 **

prediastolic   0.6177     0.1127   5.479 1.24e-05 ***

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.996 on 24 degrees of freedom

(1 observation deleted due to missingness)

Multiple R-squared: 0.5558, Adjusted R-squared: 0.5372

F-statistic: 30.02 on 1 and 24 DF, p-value: 1.241e-05

a. What is the correlation coefficient for the variables diastolic and prediastolic? ________

b. Explain to your friend the regression coefficient of 0.6177 (give units).

c. What hypotheses are being tested with the Pr(>|t|)

d. Would you conclude that a linear relationship exists between the two variables? Why?

Answer 1

a.

The correlation coefficient for the variables diastolic and prediastolic is square root of Multiple R-squared.

correlation coefficient for the variables diastolic and prediastolic = = 0.74552

b.

The regression coefficient of 0.6177 means that with one mm of increase in prediastolic pressure, the diastolic pressure would increase by 0.6177 mm.

c.

The hypotheses are being tested with the Pr(>|t|) are

For Intercept,

For prediastolic,

d.

Since the p-value of Pre-diastolic coefficient is 1.241e-05 which is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is significant evidence that the slope coefficient of the linear model is not zero and hence the linear relationship exists between the two variables.