Answer: A line of best fit is a straight line that is the best approximation of the given data. It can be represented by the equation: y = mx + b, where m is the slope (the rate of change) of the line and b is the y-intercept (the point where the line crosses the y-axis)
To find the equation for the line of best fit for a set of data, we can use the least squares method. It involves finding the slope (m) and y-intercept (b) that minimize the difference between the predicted values of y and the actual values of y.
To find the slope, we use this formula:
m = (N∑(xy) - (∑x)(∑y)) / (N∑(x^2) - (∑x)^2)
Where N is the number of data points, x is the independent variable, y is the dependent variable, ∑ denotes the sum of all the values.
To find the y-intercept, we use this formula:
b = (∑y - m(∑x))/N
After applying the formula:
m = (5*(731) - (58)(96)) / (5*(198) - (58)^2)
m = 0.957
b = (96 - 0.957*58)/5
b = -6.836
So, the equation for the line of best fit for the given data is:
y = 0.957x - 6.836
Rounded to three decimal places, the slope and y-intercept are:
m = 0.957 and b = -6.836
So the equation for the line of best fit for the given data is: y = 0.957x - 6.836.
This equation represents the line of best fit for the given data, meaning that it is the line that most closely approximates the data.
Explanation: