The print version contains all student worksheets and answer keys needed to complete the lesson. The drill is a review of the concept of slope and y-intercept in relation to a real-world situation. In this problem the slope represents the change in monthly charges for each additional video that is rented.
You also want to do this from first principles. This will require some basic Calculus as well as some linear algebra for solving a 2 x 2 system of equations.
In other words, we wish to minimize the cost function F m,b,x,y: This function is convex, so there is an optimal minimum that we can determine.
The minimum can be determined by finding the derivative with respect to each parameter, and setting these equal to 0. We then solve for m and b. The intuition behind this is that we are simultaneously finding m and b such that the cost function is jointly minimized by these two parameters.
OK, so let's find the first quantity: Next, let's tackle the next parameter: We can again drop the factor of 2 and distribute the -1 throughout the expression: Knowing that is simply n, we can simplify the above to: Now, we need to simultaneously solve for m and b with the above two equations.
This will jointly minimize the cost function which finds the best line of fit for our data points.
Doing some re-arranging, we can isolate m and b on one side of the equations and the rest on the other sides: As you can see, we can formulate this into a 2 x 2 system of equations to solve for m and b.
Specifically, let's re-arrange the two equations above so that it's in matrix form: With regards to above, we can decompose the problem by solving a linear system: To find the inverse of a 2 x 2 system, given the matrix: The inverse is simply: Therefore, by substituting our quantities into the above equation, we solve for m and b in matrix form, and it simplifies to this: Carrying out this multiplication and solving for m and b individually, this gives: As such, to find the best slope and intercept to best fit your data, you need to calculate m and b using the above equations.
Given your data specified in the link in your comments, we can do this quite easily: Therefore, the line of best fit that minimizes the error is: How you call the function is so:Write the equation for the line of best fit for the scatter plot below 10 89 Hours of Nightly TV Watching 3/4X +9 5/4X +9 A.
6 miles per hour 12 miles per hour 1/6 miles per hour 3 miles per hour Dirt Bike Racing 3 Time (minutes) 9. Below is a graph created for a . The best-fitting line is the line that lies as close as possible to all the data points. You STEP 4 Write an equation of the line that passes through the two points from Step 3.
This Use the equation of the line of fit from the above example to predict the number of alternative-. Apr 14, · Best Answer: All I know is that the line is placed so the sum of all the distances between the scatter plot points and the line is as low as possible.
I always use my TI 83+ to get the webkandii.com: Resolved. Write the equation of the line of best fit using the slope-intercept formula y=mx+b.
Show all your work, including the points used to determine the slope and how the equation was determined (59,57), (63,62) Scatter Plots and Line of Best Fit. Linear regression is a simple statistics model describes the relationship between a scalar dependent variable and other explanatory variables.
If there is only one explanatory variable, it is called simple linear regression, the formula of a simple regression is y = ax + b, also called the line of . First of all you need to inset a line chart for given table => click on Add trendline => Select Polynomial, Exponential or other trendline whichever is best fit for your scenario.
As shown in Below image.