Biometry Homework and SPSS

1. Exercise 2.166 (p. 159):

2. Exercise 10.19 (p. 583) Use SPSS (data in the excel file)

3. For each of the following, determine whether the correlation between two variables is significantly different from zero, i.e., versus . Compute the test statistic, p-value, and state your conclusion. Use .

(a)

(b)

4. A biologist is studying the levels of heavy metal contaminants among a population of the South Nakaratuan Chubby Bat. The biologist is interested in constructing a simple linear regression model to investigate the relationship between weight of an animal and the level of heavy metal contamination. In the proposed regression model the level of contaminant is the response variable and weight is the explanatory variable. The contaminant level is measured in parts per billion (ppb) and weight in grams. The SPSS output is given below. Use the output to answer the following questions.

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.921a	.848	.839	13.82229
a. Predictors: (Constant), weight
ANOVAa
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	18143	1	18143	94.96	.000b
	Residual	3247.94781	17	191.05575
	Total	21391	18
a. Dependent Variable: contaminant
b. Predictors: (Constant), weight

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
	B	Std. Error	Beta
1	(Constant)	-71.63611	28.17794		-2.54	.021
	weight	2.18277	0.22399	.921	9.74	.000
a. Dependent Variable: contaminant

(a) What percent of variation in the values of contaminant level that is explained by the linear regression model between contaminant level and weight?

(b) What is the correlation between contaminant level and weight?

(c) What is the predicted contaminant level for an animal weighted 150 grams?

(d) One of the animals in this analysis had a weight of 145 grams and contaminant level of 222 ppb. What is the residual for this observation?

(e) What is least squares regression line?

(f) What is the average change in contaminant level when the weight of an animal is increased by 1 gram?

(g) Construct a 99% confidence interval for the regression slope.

(h) The biologist wants to determine whether there is a positive linear association between contaminant level and weight of an animal. Write down the appropriate hypotheses, value of test statistic, degrees of freedom of the test statistic, p-value, and the conclusion.

5) Acute otitis media (AOM) is the most common diagnosis for which antibiotics are prescribed for children. Treatment of AOM accounts for an estimated 15 million antibiotic prescriptions written per year in the United States. Untreated AOM has a high rate of spontaneous resolution, with similar rates of complications whether antibiotics are prescribed or withheld. Resistance to antibiotics is a major public health concern worldwide and is associated with the widespread use of antibiotics. A randomized controlled trial was conducted to determine whether treatment of AOM using a “wait-and see prescription” (WASP), with which parents are asked not to fill the prescription unless the child either is not better or is worse in 48 hours, significantly reduced use of antibiotics compared with a “standard prescription” (SP). A total of 283 patients diagnosed as having AOM were randomized, with 138 patients to the WASP group and 145 to the SP group. Prescriptions were not filled for 82 patients in the WASP group and for 17 patients in the SP group. Conduct a hypothesis test to determine whether the WASP reduces the use of antibiotics than the SP. Use α = 0.01.

………..

1. (2 points) Tobacco spending is the explanatory variable, and alcohol spending is the response variable. What is the equation of the least-squares regression line?

2. (4 points) Show a scatterplot of the data. Include the least square regression line on the graph. Describe the form, direction and strength of your data.

3. (1 point) What % of the variation in alcohol spending is explained by the least squares regression line?

4. (3 points) Give a 99% confidence interval for the average rate of change of alcohol spending. (Hint: This is another way to say “slope”)

5. (3 points) Are tobacco spending and alcohol spending independent? Perform a test and state the hypotheses, P-value, and conclusion in terms of the question.

6. (3 points) Make a normal probability plot.

Do the points fall around a straight line? (Yes or No)

Does the distribution look normal? (Yes or No)

7. (4 points) Make a residual plot.

Do the residuals fall randomly around the 0 reference line? (Yes or No)

Can you find any clear pattern in the residual plot? (Yes or No)

Are there any outliers? (Yes or No)

If “Yes”, where is the outlier? Please circle the outlier point in the residual plot, (and if you have time, find its corresponding region in the dataset).