Archers need to use arrows that do not bend easily. Th e table shows how the weight of an arrow affects its spine, or the distance the center of the arrow bends when a certain constant weight is attached. Graph the data in the table to find a linear and a quadratic model for the data. Use the regression feature on your calculator to find each model. Which model is a better fit? Explain. weight (in grams) 140,150,170,175,205 weight (in inches) 1.4,1.25, .93, .78, .43 I got for quadratic a=.000057 b=-.034779 c= 5.17175 for linear i got m=-.015206 b=3.51253 what do I do now?
you have the coefficients for the models:
y = ax^2+bx+c
or
y=mx+b
sounds like you need to review more than just which buttons to push.
To graph the data and find the linear and quadratic models using the regression feature on your calculator, follow these steps:
1. Gather the given data:
Weight (in grams): 140, 150, 170, 175, 205
Weight (in inches): 1.4, 1.25, 0.93, 0.78, 0.43
2. On your calculator, locate the regression feature. It is usually denoted by a button labeled "Reg" or "Stat" on scientific or graphing calculators.
3. Select the regression type. In this case, we will perform both a linear and a quadratic regression. Check your calculator manual for specific instructions on how to choose regression types.
4. Enter the data into the calculator. Depending on your calculator, this may involve inputting the data points directly or entering them into a table.
5. Perform the linear regression and record the equation representing the linear model. You mentioned that you got the equation m = -0.015206x + 3.51253, where m represents the spine value and x represents the weight (in grams).
6. Perform the quadratic regression and record the equations representing the quadratic model. You mentioned that you got the equations:
a = 0.000057
b = -0.034779
c = 5.17175
7. Graph the data and the models on your calculator. This will help visualize the relationships between the weight (in grams) and the spine values.
Now, to determine which model is a better fit, consider the following factors:
- R-squared value: Check the R-squared value associated with each model. The R-squared value represents how well the model fits the data, with values closer to 1 indicating a better fit. Compare the R-squared values of the linear and quadratic models.
- Visual assessment: Examine the graph of the data and the models. Does one model align more closely with the data points? Pay attention to any patterns or deviations from the models on the graph.
By scrutinizing the R-squared values and visually analyzing the graph, you will be able to identify which model is a better fit for the given data.