CH2.7 Linear Curve Fitting Model By, Thanh Quotient

For my Ch. 2 Project of Linear Curve Fitting Model, My Car model was the Fusion Ford 2011. I needed to find the mileage when the speed was at (55,60,75,80,85,90), as a result, i got the numbers that corresponds the order, the numbers i had were (17,18.5,20,21.6,23,24.7). First i Plotted all of these points and i soon found that this graph had a strong positive correlation, positive correlation means positive slope. After i had my points plotted, i sketched a line of best fit. I then chose the coordinates (55,17) and (65,20) and i then used the slope formula and found that my slope was .3. I then used the slope to find the equation by using the point slope formula and then got Y=.3x + .5 and entered the formula in my graphing calculator, after that I plugged it in with all of my points entered in my stat plot i then found the correlation coefficient to be .9997842645. The correlation coefficient of r tells us how strong the correlation is. The equation i found after finding the correlation coefficient for Y was Y= .3x + .1257. Next, i needed to find the mileage for a speed of 55mile per hour, i plugged 55 in X variable of my equation. After that i found the Speed of a mileage 28, i did it by plugging in 28 in my equation again, but this time the Y variable and found that the speed was 92.9 miles per hour.

CH 2 Project

For my chapter 2 project, I chose the car Nissan Versa. So I needed to find the mileage when the speed was at (55,60,75,80,85,90). As a result, my mileage was (34,33,31,3,28.2,26.2,24.5). I later found out I had a negative correlation since it was a negative slope. When I finished that, I graphed and plotted down the points and made the line of best fit. Then I chose 2 points (55,34) and (80,24.5) and used the slope formula to find the slope which was at -.42. After that I needed to find the equation so use the point slope formula to find it and it was y=-.42x+57.1. To find the correlation coefficient I needed to use the graphing calculator to find that r=-.99. Finding r is important since it tells the higher the speed you would drive, the the mileage would be. The line of best fit would be y=-.41x+56.92. To find the mileage for a speed of 55 miles per hour I had to plug the 55 into X to get 34.37. To find the speed if the mileage is 28 I needed to plug the 28 into Y to get -70.54.

Ch 2 project- Ford Mustang

For my chapter 2 project, I chose the Ford Mustang. The mileage for the speeds: 55, 60, 65, 70, 75, and 80 were 30, 29.1, 27.6, 24.9, 23.1, and 21.6. I knew I had a negative correlation because I had a negative slope. Then I sketched the line of best fit, while trying to get as many points on the line as possible. I then chose 2 points on the graph, (80, 21.6) and (70, 24.9), and found the slope (by using the slope formula) which was -.33. Then to find the equation I had to use the point slope form, then turning it into slope intercept form and I got y= -.33x + 48. I had to use the calculator to find the correlation coefficient r and got r= -.9914. This told me that as the speed gets higher the mileage will get lower, because it’s reaching the – 1 coefficient. Also when using the calculator I was able to find the equation for the line of best fit, which was y= -.3582x + 50.2342. To predict the mileage for a speed of 55 mph, I plugged in 55 for X and solved for y and I got 30.5332 miles per gallon. To predict the speed if the mileage is28 I plugged in 28 for y and solved for x and I got 62.87202 miles per hour.

Ch 2 project-Mercedes McLaren

For my chapter 2 project, I chose the Mercedes McLaren. First, I find mileages for speeds {55,60,65,60,75,80}, which is {16,15.5,14.7,13.3,12.3,11.5}. Then I made a graph of all the numbers according to the data and it comes out with a strong negative correlation. Then I chose (15.5,60) and (16,55) and use the slope formula to find the find the slope, which is -0.1. Next, I use the point slope formula to find the equation of two points, which turns out to be y=-0.1x+21.5. Then I use the graphing calculator and graph the data and find the line of best fit with its equation and correlation coefficient. The correlation coefficient is -0.992104599 and the equation is y=-0.1914285714x+26.8047619. If the speed of the car is 55 miles per hour, then the mileage would be 16.27619047 miles per gallon. If the mileage is 28 miles per gallon, then the speed would be approximately 25 miles per hour.

CH 2. Project- Nissan GTR

Nissan GTR

For the chapter 2 project, I did it on the Nissan GTR. I used the speeds 55,60,65,70,75, and 80 the mileage (miles per gallon) are 21,20.4,19.3,17.4,16.2, and 15.1. Next, I plotted the points of a graph. For the independent variable, it was speed (miles per hour) and for the dependent variable, it was mileage (miles per gallon). As I graphed the data, it started to become a negative correlation. Then I drew the line of best fit and to find the slope, I used the two points (55,21) and (80,15.1). The slope I found was -5.9/35. When I used the point slope form, I found the equation y=-5.9x/35+11.73. When I used a graphing calculator to find the value of my graph's correlation coefficient of r was -.99 . The value of r tells us that the higher the speed is, the lower the mileage. The line of best fit equation I found with the calculator is y=-.25x+35.2. To predict the mileage for a speed of 55 miles per hour would be 21.45. To predict the speed if the mileage is 28 miles per gallon would be 28.8.

Chapter 2 Project

For the Chapter 2 project, I picked the car Honda Accord Sedan. First, I found out the mileages of this car while the speeds were (50, 55, 60, 65, 70, 75). Next, I sketched a line that best fit the graph. According to the line that going down on the graph, I found it was Negative Correlation. Then I used two points on the line to find the slope which was -0.3. Then I used the point-slope form to write an equation of the data which was y=-0.3x+36. Next, I used the graphing calculation to find correlation coefficient which was r=-0.97. The value of r tells me that the mileage will go down if the speed goes up. The equation that best fit the line was

y=-0.33x+37.02. I predict that the speed was 45.5 mph for a mileage of 22 mpg. And I predict the mileage was 22.17 mpg for a speed of 45 mph.

Ch. 2 project

For my Chapter 2 project, I chose the Lexus IS250. I had to find out the mileage for my car at these speeds : (55, 60, 65, 70, 75, 80) and for each of the speeds, the mileages were : (26, 25.2, 23.9, 21.6, 20, 18.7). I then graphed the points and the line showed that it has a negative correlation, which means that the slope is negative. Then I drew the line of best fit. To find the slope, I used the two points (55, 26) & (80, 18.7). The slope I found was -0.29. Using the point slope form, I found the equation y=-0.29x+42. The value of my graph's correlation coefficient of r is -.99. The value of r tells us that the higher the speed is, the lower the mileage would be. The line of best fit equation I found with the calculator is y=-.31x+43.5. The mileage for a speed of 55 miles per hour would be 26.45. The speed is 50 if the mileage is 28 miles per gallon.

Ch.2 Project

I have choose the MINI Cooper for my chapter 2 project. I found out the mileage for the car in http://www.mpgforspeed.com/. For the speeds 55, 60, 65, 70, 75, 80 in miles per hour, the mileage (miles per gallon) are 37, 35.9, 34, 30.7, 28.5, 26.6 . Next I plot the points using speed as the independent variables and the mileage as the dependent variables. Since the points are going down, the graph have a negative slope that mean it also have a negative correlation. Next, I sketch the line best fit on the graph. The 2 points I choose to find the slope with is (60,35.9) and (80,26.6); doing the calculation Y1 - Y2 over X1 - X2 I got the slope -9.3/20. To use the informations I already have to write an equation I set up the point-slope form first which is y-26.6=-9.3/20(x-80) turning it to slope-intercept form the equation is y=-9.3/20x+63.8 . Using the calculator to find the value of correlation coefficient r, r=-.9917995234. The value of r tell me that the as speed get higher is the mileage will go lower, because r is close -1 coefficient. By using the graphing calculator to find the equation for the line best fit I get y=-.4428571429x+62.00952381 . To predict the mileage for a speed of 55 miles per hour, I type in : y(55) in my calculator, the mileage is 38 (miles per gallon). To predict the speed if the milage is 28 miles per gallon we can't use the same method because 28 is y in the equation, so I plug 28 in as y, 28=-.4428571429x+62.00952381. After isolating x (speed) the answer is 77 miles per hour.

Ch 2 project

For this project i picked the car Mercedes Guard S600. First i found out what the mileage was while the speed was 55, 60, 65, 70, 75, and 80. I then graphed the points and since the line was going down the graph was a negative correlation. Then i drew the line of best fit. Then i used two points to find the slope and my slope was -3.9/20. Then i used the point slope form to write my equation y=-3.9/20x+-6.275. I used the graphing calculator to find the correlation coefficient which was r=-.9921. I think the value of r tells the faster you drive the mileage will go down. The equation for best fit is y=-.204x+28.52. I predict that the mileage for a speed of 55 mph is 17 mpg. I also predict that the speed if the mileage is 28 mpg will be about 30mph.

Ch.2 Project

For my Chapter 2 project, i picked Toyota Highlanders as my car. The speed in miles per hour is (55, 60, 65, 70, 75, 80), and the mileage in miles per gallon is (23, 22.3, 21.2, 19.1, 17.7, 16.6).
I used the data to make a scatter plot graph and it came out to be a Negative Correlation. Then I sketched the Line of Best Fit and used 2 points that lies on the line to find the Slope. The two points that i used are (60, 22.3) and (75, 17.7) and the slope came out to be -4.6/15. Next i used the Point-Slope form to find the equation that models the data and the equation is Y= -4.6/15X + 40.7. Next comes the work of a graphing calculator. I used the graphing calculator to find the Correlation Coefficient of R which is R= -0.99. The correlation coefficient tells us that the faster you drive, the mileage will be lower. The equation i found using the graphing calculator for the line of best fit is Y= -0.27X + 38.45. I Predicted that the mileage for a speed of 55 miles per hour is 23 miles per gallon. Lastly. I predicted the speed if the mileage is 28 miles per gallon would be 41.41 miles per hour.

Ch.2 Project

For my Ch.2 project, My car is the Subaru Impreza Sti. The speed or miles per hour is 55,60,65,70,75,80 and the mileage or miles per gallon is 29,28.1,26.7,24.1,22.3,20.9. Our scatter plot shows a negative correlation, because we sketched the line of best fit. The two points that I used to find the slope (55,29) and (80,20.9) and the slope is -8.1/25x. Using the point slope form, the slope intercept form is y=-8.1/25x - 11.18. By using a graphing calculator, the value of the correlation coefficient of R = -.989. The value of R tells us that the faster you drive, the lower the miles would be per gallon. The equation I found for the line of best fit is y= -8.1/25x - 11.18. My prediction of mileage for a speed of 55mph is 29 mileage. My prediction of speed for the mileage of 28mpg is 60mph.

Ch 2 Project

For my Ch. 2 Project. I picked the car model Ferrari California. First I found out the mileage (miles per gallon) as the speed is at 55,60,65,70,75,and 80. Then I plotted the points on the graph. The graph was a negative correlation so it was going to have a negative slope. Then I drew the line of best fit. I found out the two points of the line of best fit and found the slope to be -5.3/25x. Then I used the point-slope form(y-y1=slope(x-x1) to write an equation. It turned out to be y=-5.3/25x+30.66. I plugged in all the plots to my graphing calculator to find out the correlation coefficient r(R=1 is postivite and R=-1 is a negative) and it was R=-.991. The R value tells that if you drive faster miles per gallon goes down, and that the graph is a negative correlation with almost a -1 coefficient, which is a straight negative line. I found that in the calculator the line of best fit(y=ax+b) was; a=-.2262857143, b=21.77428571. I plugged in if the speed of the car goes 55 miles per hour it would be -5.3/25(55)+30.66 which equals to 19 mpg and my prediction if the speed is 28 miles per hour it would be 40mph