Question

Using the following data taking out of R (summary):

Call:
lm(formula = dys_detect ~ fin_loss, data = Lab5, na.action = na.exclude)

Residuals:
Min 1Q Median 3Q Max
-582.66 -274.75 13.53 273.92 589.06

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 385.362 77.360 4.981 8.72e-07 ***
fin_loss 3.248 1.523 2.133 0.0334 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 316.6 on 498 degrees of freedom
Multiple R-squared: 0.009052,   Adjusted R-squared: 0.007062
F-statistic: 4.549 on 1 and 498 DF, p-value: 0.03342

Use the above data to answer the following questions:

1. How much of the variability in financial loss can be explained by the number of days it takes to detect the breach?

2. What is the strength of the relationship between the predictor and outcome?

Answer 1

(1)using the given data table

we can see that r^2 = 0.009052

r^2 tells us about the percent of variation in y variable that can be explained by the independent variable x

or 0.009052*100 = 0.9052

so, we can say that

0.9052 % variability in financial loss can be explained by the number of days it takes to detect the breach

(2) correlation coefficient = sqrt(r^2)

= sqrt(0.009052)

= 0.0951

this value is very close to 0, so we can say that the strength of association or relationship between the predictor and outcome is very weak or negligible