Question

A researcher has examined the relationship between the number of hours driven by long-distance truckers in a 24-hour period (X) and reaction time in seconds (Y) at the end of the 24-hour period. The relationship is approximately linear and the correlation between the two measures is +0.43. In order to assess the usefulness of the independent variable as a predictor of reaction time, the research team determined that the regression line was given by the following: Y’ = -2.5 + 3.16X

(a) What reaction time in seconds would you predict for a driver who had logged 8.5 hours? Provide a verbal conclusion to answer this question. (You do not need to show any of your calculations.)

(b) Fully describe the association between the number of hours driven by long-distance truckers and reaction time.

Answer 1

Solution:-

Given that

A researcher has examined the relationship between the number of hours driven by long-distance truckers in a 24-hour period (X) and reaction time in seconds (Y) at the end of the 24-hour period. The relationship is approximately linear and the correlation between the two measures is +0.43. In order to assess the usefulness of the independent variable as a predictor of reaction time, the research team determined that the regression line was given by the following:

Y’ = -2.5 + 3.16X

a) What reaction time in seconds would you predict for a driver who had logged 8.5 hours? Provide a verbal conclusion to answer this question. (You do not need to show any of your calculations.)

Y’ = -2.5 + 3.16x

x = 8.5

Reaction time = -2.5+3.16*8.5

= 24.36

b) Fully describe the association between the number of hours driven by long-distance truckers and reaction time.

Number of hours driven by long-distance truckers and reaction time are moderately positively correlated since correlation between the two measures is +0.43.

With one unit increase in distance, reaction time increases by 3.16 units (Slope of regression equation = 3.16).

Thanks for supporting...

Please give positive rating...