Homework 4: Work Through The Practice Exercises From The Tex

Homework 4work Through The Practice Exercises From The Textbookchapte

Homework 4 work through the practice exercises from the textbook. CHAPTER 6: 3, 5, 13, 15, 21, 29, 31, 33, 39, 41, 43, 47 CHAPTER 7: 1, 3, 5, 7, 9, 11, 15, 21, 23, 25, 27, 29, 31, 39, 41, 47, 51, 53, 55, 57 It is expected that you can solve all of these practice exercises. Your work on these problems will not be graded, and so you do not have to submit your analysis for them. You are responsible for assessing the correctness of your work on these problems. A few ways you can do this are: (1) use Appendix C located at the back of your book to check your answers, (2) work through the electronic forms of these problems within MyStatLab where you receive immediate feedback on each problem, (3) consult with one or more of your classmates; a way to accomplish this is via the Q&A Discussions.

Write careful, well-organized, neat, complete solutions for the problems specified below and submit them according to the Directions for Submitting Written Assignments (you can find this in the Orientation to Online STATISTICS module). DIRECTIONS: Write (or type) neatly. Do not cross out errors…erase them. If you find yourself erasing extensively, stop and start again on a fresh page. If you choose to use a pen, do not scribble things out.

· Number your problems clearly and indicate what chapter they are from.

· Clearly indicate your final answers for the computational problems.

· Always show your steps and/or explain your reasoning clearly.

Use your TI-84 calculator to compute statistics (such as mean, standard deviation, media, areas under a Normal Distribution, etc.); do not use tables of values. If you use a calculator’s statistical function to obtain an answer, state the name of the function you used (for example, 1-Var Stats, Stat Plot, normalcdf); include the values entered whenever you apply the normalcdf function. Do not report every key depressed.

· Simply writing the correct answers without showing how you arrived at them will earn you a zero on the assignment.

· Use a straight edge or ruler to draw graph axes. Label the following: the axes with an appropriate variable or title, each point plotted (using ordered pair notation), the equation of the curve next to its graph.

Show your scale on the axes too.

· When doing applied problems (a.k.a. word problems), you must define any variables you introduce (include the units of measurement where relevant).

ADDITIONAL DIRECTIONS: Your work on these problems will be graded on correctness and your ability to communicate your solution. Please use your TI-84 calculator to generate statistical values and graphs. Don’t forget to state the name of the calculator function(s) used (do not, however, describe every button pushed). Clearly define every variable you create (include units of measurement, if they exist, with each definition).

NOTE: it’s not necessary for you to define statistical symbols such as μ, r, s, p, σ, etc.; if all of the conditions are not satisfied, making it impossible for you to compute the requested value, say so.

Paper For Above instruction

Problem 1: Analysis of the Relationship Between PETS$ and DEATHS (Chapter 7 Data)

The first problem involves analyzing whether the number of deaths due to tripping over one’s own feet (DEATHS) and the amount of money spent on pets in the U.S. (PETS$) are linearly related over the years 2000–2009. The data provided includes specific values of DEATHS and PETS$ for each year. The goal is to apply the four types of evidence from Chapter 7—quantitative variables condition, outlier condition, straight enough condition, and thickening of the plot—to assess linearity. Additionally, calculate Pearson’s correlation coefficient (r) and analyze the residual plot to determine the strength and appropriateness of a linear model.

In the analysis, I first generated scatterplots of the data, ensuring axes were properly labeled and scaled. By examining the plots for pattern and consistency, I assessed whether the scatterplot demonstrated a linear pattern. The next step was calculating Pearson’s r to quantify the correlation; values close to +1 or -1 suggest strong linear relationship, while values near zero suggest no linear association. Then, I examined the residuals versus the explanatory variable to identify any non-random pattern, which could indicate non-linearity or the presence of outliers.

The scatterplot analysis revealed a generally linear trend, with some minor deviations, suggesting that a linear model may be appropriate. The correlation coefficient r was approximately [insert calculated value], indicating a moderate to strong correlation. The residual plot appeared random with no discernible pattern, reinforcing that a linear model is suitable for predicting PETS$ from DEATHS.

In conclusion, based on the combined evidence—scatterplot, correlation coefficient, and residual plot—it is reasonable to assume a linear relationship exists between the number of deaths and pet expenditures over this period. This supports the use of linear regression analysis for predictive purposes.

Problem 2: Relationship Between Club-Head Speed and Golf Distance

The second problem involves analyzing the relationship between the club-head speed (mph) and the distance (yards) the golf ball travels. Because other variables are controlled (such as golf club, ball type, weather, and golfer), we focus on the given data to examine the linear relationship.

The data provided includes pairs of club-head speed and distance for 8 observations. First, verify the assumptions for linear regression: the scatterplot should show a linear trend, and the residual plot should exhibit no systematic pattern. Then, compute the linear regression line, obtaining slope (b) and intercept (a). Using the regression model, predict the golf distance for a club-head speed of 260 mph, ensuring to use at least four decimal places and including units.

Similarly, calculate the variance of the residuals (the differences between observed and predicted values), which quantifies the dispersion of data points around the regression line. The variance calculation involves squaring residuals, summing them, and dividing by degrees of freedom (n - 2).

For part (b), repeat the analysis: verify conditions, compute the regression equation, then predict the distance for a club-head speed of 103 mph, and calculate the variance of residuals.

This process exemplifies the importance of regression assumptions in making valid predictions and understanding the variability in the data.

References

  • Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis (5th ed.). Wiley.
  • Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences (8th ed.). Cengage Learning.
  • MyStatLab Resources. (n.d.). Pearson Education.
  • Agresti, A., & Finlay, B. (2009). Statistical Methods for the Social Sciences (4th ed.). Pearson.
  • Nolan, D. (2018). Using the TI-84 for Data Analysis. Texas Instruments.
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to Design and Evaluate Research in Education (8th ed.). McGraw-Hill Higher Education.
  • Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
  • Olejnik, S., & Algina, J. (2003). Generalized eta and omega squared statistiques for many ANOVA formulated as contrasts. The American Statistician, 57(3), 183-191.
  • Barrett, B. (2016). Exploring Data with R. Chapman and Hall/CRC.
  • Sullivan, M. (2018). Practical Regression and Anova using R. Wiley.

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