STT 231 Extra Credit (5 Points)

STT 231 Extra Credit (5 Points) Due Date: Monday April 18, 2016 in Class Submission after class on April 18 will not be accepted.

How well can hand-size predict height?

NAME: ______PID______

Instruction: Your answers to all questions must be typed. Copy/paste graphs next to each question in the space provided. Hand drawn graphs or hand written answers are not acceptable. Staple all your papers before submitting.

Recall the hand-length, hand width and height activity. You measured and recorded your hand length, hand width and height. The collected data is included here.

Note: Before you start your project, think about issues related to gender and measurement units. Not addressing these will have significant impact on your analysis Attached a revised data set with your project. Without such data set, your project will not be valid.

1. Draw a histogram for the height. Attach a computer print out with your homework. Clearly label it as “Height Histogram”.

[If you use Minitab: Go to Graph, choose Histogram), choose Simple, Select variable, Height. OK.]

Comment on the distribution shape of height:

______

2. Obtain the summary statistics for Hand Length, Hand Width and Height. [Go to stat, Basic Statistics, Display Descriptive Statistics, Select variables (usually continuous data), OK.] Variables N Average Median Range Variance Standard Deviation Hand Length Hand Width Height 1 3. Draw a side-by-side scatterplot between Height (Y) Vs. Hand Width (X), and Height Vs. Hand Length. Attach computer print out. [Graph, Scatterplot, Simple, OK, Enter Height for Y, Hand_Width for X, In the second row, enter Height for Y and Hand_Length for X. Multiple Graph, select ‘In separate Panels of the same graph, OK]

4. (a) Based on the scatter plot in (3), comment on the relationship between Height and Hand Width (highly positive, moderate positive, little correlation, moderate negative, etc.) ______

(b) Based on the two scatterplots, do you think the correlation of Height Vs. Hand Width is higher than the correlation of Height Vs. Hand Length? ______

Why? ______

(c) Compute the correlation coefficient Between Height Vs. Hand Width: ______

(d) Compute the correlation coefficient Between Height Vs. Hand Length: ______[Minitab Command: Stat, Basic Statistics, choose Correlation, select variables Height, Hand_width, Hand_Length, OK.]

(e) Based on the two scatterplots, do you think the correlation of Height Vs. Hand Width is higher than the correlation of Height Vs. Hand Length? ______

Why? ______

2 5. Fit a regression line to predict Height using Hand Width, and report the following results: [Stat, Regression, choose ‘Fitted Line Plot’, Response (Y): Height Predictor (X): Hand_width, Click on ‘Graph’ choose ‘Four in One’. Click OK. Click on ‘Storage’, select ‘Residual’, OK, OK]

(a) Regression Line: ______(b) Copy and paste the scatter plot with the fitted line:

(c) Predict an individual’s height if hand width is 8.5’’: ______

(d) Can you predict an individual’s height if his hand width is 20”? Why?

(f) Suppose an individual has height 72” and hand width 9.0”.

Using the model to predict his height: ______, what is the corresponding residual : ______