Ch. 9 Pretest Correlation & Residuals
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1 Ch. 9 Pretest Correlation & Residuals Name Period 1. The number of students in a school chorus has increased since the school first opened 6 years ago. Predicted # Residual a) Find the Linear Regression Equation Year # of Students of Students Value b) Interpret the Regression Equation c) Find the correlation coefficient. d) Interpret the correlation coefficient. e) Fill in the table above with the predicted # of students (using your regression equation) and the Residual Values for the years listed. f) Construct a scatter plot and sketch the g) Construct a Residual Plot using the line of best fit. the table h) Based on the residual plot do you think a linear model is a good fit? Why?
2 2. The weekly sales of an album have increased since it was first sold at a music store 6 weeks ago. Week # of Albums Sold Predicted # of Albums Sold Residual Value a) Find the Linear Regression Equation b) Interpret the Regression Equation c) Find the correlation coefficient d) Interpret the correlation coefficient. e) Fill in the table above with the predicted # of albums sold (using your regression equation) and the Residual Values for the years listed. f) Construct a scatter plot and sketch the g) Construct a Residual Plot using the line of best fit. the table h) Based on the residual plot do you think a linear model is a good fit? Why?
3 3. While in high school, Claudia started her own T-shirt printing business. The table shows the number of T-shirts Claudia has sold each year since starting his business in Year # of T-shirts Predicted # of T-shirts Residual Value a) Find the Linear Regression Equation b) Interpret the Regression Equation. c) Find the correlation coefficient. d) Interpret the correlation coefficient e) Fill in the table above with the predicted # of albums sold (using your regression equation) and the Residual Values for the years listed. f) Construct a scatter plot and sketch the g) Construct a Residual Plot using the line of best fit. the table h) Based on the residual plot do you think a linear model is a good fit? Why?
4 4. What is the difference between interpolation and extrapolation? 5. The table shows the population decline of a small town over a seven-year period. Year Population (Thousands) a. Determine the linear regression equation (with 2005 being year 0) b. Interpret the equation in terms of the problem situation. c. Predict the population of the town in 2014 using your regression equation. d. Do you think your prediction seems reasonable? Explain. e. Predict the population of the town in 2090 using your regression equation. f. Do you think your prediction seems reasonable? Explain. g. Predict the population of the town in 2010 using your regression equation. Is this interpolation or extrapolation? h. Predict the population of the town in 2000 using your regression equation. Is this interpolation or extrapolation? 6. Sketch multiple examples of residual plots that indicate a linear model: a. may be appropriate for a data set. b. may not be appropriate for a data set. 7. Explain how to find the residual value and what it represents.
5 8. Sketch an example of a scatter plot with: a. positive correlation. b. negative correlation. c. no correlation. 9. What correlation coefficients (r-value) are most appropriate (accurate) for a a. positive correlation? b. negative correlation? c. no correlation? 10. Sketch a line of best fit and write a possible linear regression equation for each scatterplot. a. b. c. d. For each of the three scatterplots above, estimate what you think the correlation coefficient might be for your regression equation and EXPLAIN your reasoning. 13. Write an equation of the line that goes through the following points: a. (3, 4) and (0, 5) b. ( 2, 6) and (4, 7) c. (3, 4) and (5, 8)
6 11. Graph the following systems of equation, and estimate the solution using the graph: a. y = 2 x 4 3 b. y = 1 x c. 2x y = 6 d. y = x 1 y = 4 x = 3 y = 3x + 1 y = 2 x Solve each of the following equations for x: a. 2x + 1 = 5x b. 4x 3x + 9 = 12 c. 10x 1 = 7x 3 d. 5 4(2x + 3) = 3x 4 e. 10 x (2 + 4x) = 90 4x + x f. 2x 4 = 4 g. x 4 = 24
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