Question

Construct a scatter plot. Find the equation of the regression line. Predict the value of y for each of the x-values. Use this resource: Regression Give an example of two variables that have a positive linear correlation.

Give an example of two variables that have a negative linear correlation.

Give an example of two variables that have no correlation.

Height and Weight: The height (in inches) and weights (in pounds) of eleven football players are shown in this table.

Height, x 62 63 66 68 70 72 73 74 74 75 75 Weight, y 195 190 250 220 250 255 260 275 280 295 300

x = 65 inches x = 69 inches x = 71 inches

Answer 1

Scatter plot

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I have used minitab software for regression line

1. Enter the data
2. Stat
3. regression
4. regression
5. Fit regression model
6. Select 'Weight(y)' as response and 'Height(x)' as continuous predictor
7. ok

The minitab output

hence the resression line

Weight(y) = -257.3038 + 7.2544 Height(x)

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From the above regression line ,for

x = 65 inches,y=214.227 pounds

x=69inches,y=243.245 pounds

x=71 inches,y=257.754 pounds

and for the rest values of x we have

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an example of two variables that have a positive linear correlation or r>0

Marks of 10 students in mathematics and statitics

covariance of (x,y)=213.84

var(x)=180.56,var(y)=289.56

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an example of two variables that have a negative linear correlation or r<0

The following table gives the index numbers industrial production in a country and the number of registered unemployed persons(in thousands) in the same country during the eight consecutive years.

cov(x,y)=-44

var(x)=6,var(y)=952

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an example of two variables that have no correlation or r=0

cov(x,y)=0

hence r=cor(x,y)=0

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