Question: A data has \(n=20, \Sigma x=8552, \Sigma y=398.2, \Sigma x^{2}=5196, \Sigma y^{2}=9356, \Sigma x y=216.6\).

Assuming that \(x\) and \(y\) are related linearly and the simple linear regression model is appropriate,

1. Find the least squares estimates of slope and intercept of model.
2. What is the fitted value for \(x=5\) ?
3. Compute the sample correlation coefficient of \(X\) and \(Y\).
4. Test
   H0: population correlation \((X, Y)=.80 \quad\)
   H1: population correlation \((X, Y)>.80\)
   Use \(a=.05\)
5. Find \(95^{\text {th }}\) percentile of the distribution of \(Y\) when \(x=5\)

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