Consider the values for the dependent and independent variables shown to the right. a. Develop a scatter plot of the data. Does the plot suggest a linear or nonlinear relationship between the dependent and independent variables? b. Develop an estimated linear regression equation for the data. Is the relationship significant? Test at an ? = 0.05 level. c. Develop a regression equation of the form ? = b0 + b1 ln (x). Does this equation provide a better fit to the data than that found in part b? x y 5 10 9 30 13 39 18 43 23 45 27 46 a. Which scatter plot below shows the data? Does the plot suggest a linear or nonlinear relationship between the dependent and independent variables? A. The plot suggests a negative linear relationship because the y-values decrease as the x-values increase. B. The plot suggests a positive linear relationship because the y-values increase as the x-values increase.
Added by Chris R.
Close
Step 1
Step 1: Based on the scatter plot provided, it suggests a linear relationship between the dependent and independent variables. Show more…
Show all steps
Your feedback will help us improve your experience
David Nguyen and 83 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Madhur L.
What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a linear relationship between x and y. Try to approximate the relationship between x and y by drawing a straight line through the data. Select your answer to provide a linear approximation of the relationship between x and y. Develop the estimated regression equation by computing the values of b0 and b1 using equations: (Enter negative values as negative figures) Σ(xi)(yi) Σ(xi^2) b0 = y - b1 (2 decimals) Use the estimated regression equation to predict the value of y when x = 12. (2 decimals)
Sri K.
For each of the following data sets, a. Create a scatterplot. b. Use $\operatorname{LinReg}(\text { ax }+\text { b) to determine the best fit line and } r .$ Does the line seem to accurately describe the pattern in the data? c. For each of the different choices listed in the above chart, find the equation of the best fit curve and its associated $r^{2}$ value. Of all of the curves, which seems to provide the best fit? Note: The $r^{2}$ -value reported in each case is NOT the linear correlation coefficient reported when running $\operatorname{LinReg}(\mathrm{ax}+\mathrm{B})$ Rather, the value will typically change depending on the curve. The reason why is that each time, the $r^{2}$ -value is measuring how accurate the fit is between the data and that type of curve. A value of $r^{2}$ close to 1 still corresponds to a good fit with whichever curve you are fitting to the data. $$\begin{array}{|c|c|} \hline x & y \\ \hline 0.5 & 1.20 \\ \hline 1.0 & 0.760 \\ \hline 1.5 & 0.412 \\ \hline 2.1 & 0.196 \\ \hline 2.9 & 0.131 \\ \hline 3.3 & 0.071 \\ \hline \end{array}$$
Review: Equations and Inequalities
Linear Regression: Best Fit
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD