Question

Linear Regression and Prediction perform a linear regression to determine the line-of-best fit. Use weight as your x (independent) variable and braking distance as your y (response) variable. Use four (4) places after the decimal in your answer.

Sample size, n:     21
Degrees of freedom: 19

Correlation Results:
Correlation coeff, r: 0.3513217
Critical r:           ±0.4328579
P-value (two-tailed): 0.11837

Regression Results:
Y= b0 + b1x:
Y Intercept, b0:      125.308
Slope, b1:            0.0031873

Total Variation:       458.9524
Explained Variation:   56.6471
Unexplained Variation: 402.3053
Standard Error:        4.601517
Coeff of Det, R^2:     0.12342

What is the equation of the line-of-best fit (linear regression equation)? Present your answer in y = bo + b1x form. Y=b0+b1x

Answer 1

Answer

We know that the equation of the line-of-best fit (linear regression equation) is given as

y = bo + b1*x

where bo is intercept of the linear equation and b1 is the slope of linear equation

Using the data given in the question, it is clear that the value of bo is 125.3080 and b1 is 0.0032

This means that the required equation of the line of best fit is y = 125.3080 + 0.0032x

This equation shows that the slope value is positive, which means for every one unit increase in the value of x, there will be an increase of 0.0032 unit in the value of y.