Part II: ( 10 points )

Galileo was 31 years old when he began conducting a series of experiments and writing a treatise concerning the path of projectiles. He was 42 years old when he completed these studies; at last giving an explicit formulation for the motion of falling bodies. The primary experiment was performed with an inclined ramp elevated a certain height from the floor and a ball that served as the projectile. The ball was released at a set height on the ramp and allowed to roll down a groove set into the ramp. When the ball left the ramp’s edge, it began its descending flight at a speed depending on the release height. The measurement of release height (H) and distance traveled (D) before landing was recorded. The units of measurement are punti (points) and the data are shown below.

We will consider fitting a linear model to these data. Enter the data into SPSS and obtain the output for a linear regression, including a scatterplot of residuals plotted versus predicted values (include a fit line), a residual histogram, a normal probability plot, descriptive statistics, R square change, and 95% confidence intervals for the parameters.

1. Interpret both the R and the Adjusted R ² values (Note: Just for the R, state the null and alternative hypotheses for it and also the tabled critical value at the .05 alpha level, two-tailed test) (2).
2. List and interpret the standard error of the estimate (1).
3. For the F test, state the null and alternative hypotheses for it and also the tabled critical value at the .05 alpha level. What does the F test result indicate about the regression model (1)?
4. For the test of the slope, state the null and alternative hypotheses for it and also the tabled critical value at the .05 alpha level, two-tailed test. What does the t value for the slope tell you (1)?
5. List the confidence interval for the slope and what does it indicate (1)?
6. List and interpret the values for both the slope and the y-intercept (2).
7. Print and interpret the graph that produces the distribution of the residuals for the regression model, along with the values associated with the Cook’s Distance (i.e., the maximum) and Durbin-Watson tests (2).

Part III : ( 10 points )

Using the SPSS data set provided on LiveText labeled "Lab 3 Fall," run a Crosstabs procedure on Q1 and gender, where you are trying to test if there is an association between the two variables (10 points):

1. State the null and alternative hypotheses, note the tabled critical value of the chi-square at the .05 alpha level, the value of the sample test statistic, the sample p-value, and state the conclusions that can be reached (3).
2. What do the standardized residuals tell you about your result from question 1? (1).
3. What effect size should we use in this instance and explain what its value is telling us (2)?
4. Check the assumptions for this test, print out a bar chart of the data, and discuss whether the assumptions are fine for these data. (2).

In reviewing the results and assumptions, which is the better test, chi-square or Yates’ continuity correction, to run in this situation and explain why

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