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## Hypothesis test for correlation coefficient.

Use the following data set for prices for custom homes comparing square feet (in hundreds) and price (in thousands).

 Square Feet Price 26 259 27 274 33 315 29 296 29 325 34 380 30 359 40 523 22 215

a.Construct a scatterplot for this data set in the region to the right.

b. Based on the scatterplot, does it look like a linear regression model is appropriate for this data?  Why or why not?

C. Add the line-of-best fit (trend line/linear regression line) to your scatterplot.  Give the equation of the trend line below.

D. Use your trend line to predict the cost of a home with 2300 (23) square feet.

E. Determine the value of the correlation coefficient.  Explain what the value tells you about the data pairs?

F. Does the value of the correlation coefficient tell you there is or is not statistically significant evidence that correlation exists between square feet and price of custom homes?  Explain your position.  (HINT: application of table A-6 is needed!)

G. What percent of the variation in cost can be explained by the regression line in regard to knowing the square footage?  (HINT:  review the meaning of the coefficient of determination value)

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