Archers need to use arrows that do not bend easily. The 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 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 0.93 0.78 0.43
Can someone please help me with this problem I'm totally lost.
Plot the points (140, 1.4); (150, 1.25); (170, 0.93); (175, 0.78); (205, 0.43) on your graphing calculator; Use your calculator manual to find out how to fit this data to a straight line (linear model), and then a quadratic equation (quadratic model) Look at the results; which has a better fit? Do the data look like they are in a straight line, or more like points on a parabola?
Must feel good to feel like seventh grade again. I do not envy you tainkg Algebra although I remember it with more fondness than Geometry which just about did me in.Maria
Did anyone ever find the answer? I also need help with this
To graph the data and find linear and quadratic models, you can follow these steps:
1. Input the given data into a graphing calculator or software.
2. Plot the points on a scatter plot, with weight (in grams) on the x-axis and weight (in inches) on the y-axis.
3. With the points plotted, use the regression feature on your calculator to find the linear and quadratic models for the data.
Now let's go through these steps to find the linear and quadratic models and determine which one is a better fit.
Step 1: Input the data into a graphing calculator or software:
x-values (weight in grams): 140, 150, 170, 175, 205
y-values (weight in inches): 1.4, 1.25, 0.93, 0.78, 0.43
Step 2: Plot the points on a scatter plot:
(Note: The scatter plot is a visual representation of the data, where each point represents a weight in grams and its corresponding weight in inches.)
Step 3: Use the regression feature on your calculator to find the linear and quadratic models:
Linear model:
A linear model can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.
Quadratic model:
A quadratic model can be represented by the equation y = ax^2 + bx + c, where a, b, and c are coefficients.
Use the regression function on your calculator to find the linear and quadratic models.
The regression results will provide you with the equations for both models.
Step 4: Determine which model is a better fit:
To determine which model is a better fit, consider the following factors:
1. Coefficient of determination (R-squared value): This value ranges from 0 to 1 and represents the proportion of the variance in the dependent variable (weight in inches) that can be explained by the independent variable (weight in grams). A higher R-squared value indicates a better fit.
2. Visual inspection of the scatter plot: Compare the scatter plot points with the line or curve of the model. A model that closely matches the points suggests a better fit.
By evaluating these factors, you can determine which model (linear or quadratic) is a better fit for the given data.