Module 5 Homework Assignment The paired data below consists of test scores and h

Question

Module 5 Homework Assignment

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. Use this data set to answer the questions below:

x   Hours of preparation 5 2 9 6 10

y   Test score       64 48 72 73 80

1. Use the given data to find the correlation coefficient r, regression equation and scatter plot in MS Excel.

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2. Based on the linear correlation coefficient r, is this a good model? Explain.

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3. What is the best predicted test score for a student who spent 7 hours preparing for the test?

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4. Find the standard error . Use formula or MS Excel.

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5. Find the 99% prediction interval for the test score of a person who spent 7 hours preparing for the test given that E=34.677. Interpret the result.  

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6. Find the explained variation.

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7. Find the unexplained variation.

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8. Find the total variation.

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9. Find the value of r2 and explain its meaning.

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10. If the data point ( 3, 100) is added to the data set, how would this effect the results of the regression analysis? Is this data point an outlier, influential point or both? Explain.

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Explanation / Answer

1.

Step 1: Find XY , X2 and Y2 as it was done in the table below.

Step 2: Find the sum of every column to get:

X=32 , Y=337 , XY=2302 , X2=246 , Y2=23313

Step 3: Use the following formula to work out the correlation coefficient.

r  = nXYXY/[nX2(X)2][nY2(Y)2]= 5230232337/[5246322][5233133372]0.9241

2. As r is near to 1 it is a good model

3. We will first find regression equation

Step 1: Find XY and X2 as it was done in the table below.

Step 2: Find the sum of every column:

X=32 , Y=337 , XY=2302 , X2=246

Step 3: Use the following equations to find a and b:

a=YX2XXY/nX2(X)2=337246322302/524632244.845

b=nXYXY/nX2(X)2=5230232337/5246(32)23.524

Step 4: Substitute a and b in regression equation formula

y  = a + bx= 44.845 + 3.524x

Now for x=7, y=69.513

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Ybar=67.4

So SE=sqrt(Yi-Ybar)^2/n-1=sqrt(599.2/4)= 12.24

X Y XY XX YY   5 64 320 25 4096 2 48 96 4 2304 9 72 648 81 5184 6 73 438 36 5329 10 80 800 100 6400

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