The equation of the line that best fits the data in slope-intercept form is y ≈ 785.4545x + 1909.0909, and the corresponding r² value is 0.861.
How to construct a scatter plot
To construct a scatter plot and find the equation of the line that best fits the data, use the given values:
X: 0.1, 0.1, 2.6, 3.7, 3.8, 5, 6.7, 7.9, 8.5, 9.4
Y: 2000, 2000, 3000, 4000, 4000, 5000, 6000, 7000, 8000, 8000
Plot the data points on a scatter plot:
The plotted graph is attached as image
Now, find the equation of the line that best fits the data. Use linear regression to estimate the slope and intercept of the line.
The equation of a line in slope-intercept form is given by:
y = mx + b,
where m is the slope and b is the intercept.
Using statistical calculator, the estimated equation of the line is:
y ≈ 785.4545x + 1909.0909
The estimated slope is 785.4545, and the estimated intercept is 1909.0909.
To assess how well the line fits the data, calculate the coefficient of determination (r²).
The coefficient of determination measures the proportion of the variance in the dependent variable (y) that can be explained by the independent variable (x).
A higher r² value indicates a better fit.
Using the same calculator that performed the linear regression, the r² value for the line that best fits the data is 0.861
Therefore, the equation of the line that best fits the data in slope-intercept form is y ≈ 785.4545x + 1909.0909, and the corresponding r² value is 0.861.
Construct a scatter plot. Find the slope-intercept form of the equation of the line that best fits the data and its r² value.
X: 0.1, 0.1, 2.6, 2.6, 3.7, 3.8, 5, 6.7, 7.9, 8.5, 9.4
y: 2000, 2000, 3000, 4000, 4000, 5000, 6000, 7000, 8000, 8000