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Advanced Statistics

Pretend that you want to study the linear relationship between voltage and current. Pick a sample of seven readings on seven different days (pick numbers of your own choice).

a. Graph the scatter plot.

b. Compute the value of the correlation coefficient.

c. Test the significance of the correlation coefficient. Use alpha equal to 0.05

d. Find the equation of the regression line.

e. Plot the regression line.

f. Find the residuals.

g. Graph the residual plot.

h. Find the three types of variation.

i. Find and interpret the coefficient of determination.

j. Find the sum of the squares of the residuals (least square).

k. Calculate and interpret the standard error S.

1. Test whether a linear relationship exists between x and y.

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Advanced Statistics

(2) If ABCD is a parallelogram such that M2ABC = 30. Show that DM >AM where M is the point of the intersection of the two diagonals of the parallelogram.

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Advanced Statistics

(1) If ABCD is a quadrilateral such that AC - BD. Show that the quadri-lateral PQRS is a rhombus where P,Q, R and S are the midpoints of the sides of the quadrilateral ABCD.

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Advanced Statistics

9) Find the standard deviation of your 250 sample means. What value should it be,according to the central limit theorem? Was it what you would expect?

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Advanced Statistics

8) Find the mean of your 250 sample means. What value should it be, according to the central limit theorem? Was it what you would expect?

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Advanced Statistics

7) Discuss the histogram shape. Create a normal probability plot for the sample means. Does the Central Limit Theorem seem to be working?

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Advanced Statistics

6) Make a histogram of your 250 sample means using bins 5 units wide.

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Advanced Statistics

5) For each sample, calculate the mean. (There should be 250 sample means.)

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Advanced Statistics

4) Make a histogram of 7500 integer values you generated. Use bins 10 units wide.Describe the shape of this distribution and calculate the sample mean and SD from the data you generated. Are these values similar to the theoretical values you found in (3)?

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Advanced Statistics

3) What theoretical distribution are you using when you do this? What are the mean and SD of this theoretical distribution?

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