Question

A new computer circuit was tested and the times (in nanoseconds) required to carry out different subroutines were recorded.

Difficulty 1 3 3 4 5 6 6 6
Time 10 11 12 9 15 19 21 18
Find the regression line for the data. Assume x is the difficulty level and y is the time. (Round your values to four decimal places.)

Answer 1

To find the regression line for the data, calculate the slope and y-intercept using the given formulas.

Step-by-step explanation:

To find the regression line for the data, we need to calculate the slope and y-intercept of the line that best fits the data points. The equation of a regression line is y = mx + b, where m is the slope and b is the y-intercept. Using the given data, we can calculate the slope using the formula:

m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)

And the y-intercept using the formula:

b = (Σy - mΣx) / n

Substituting the values into the formulas, we can find the regression line for the data.

A regression line is a straight line that best represents the relationship between two variables in a scatterplot. It's often used in statistics to model and analyze the relationship between a dependent variable (often denoted as "y") and one or more independent variables (often denoted as "x").