Math Solutions

[Solution] Consider the following bivariate data that reflects a linear model: x 2 4 6 8 10 y 8 2 -8 -18 -24 Construct the linear regression model y#770;=b_0+b_1x

Question: Consider the following bivariate data that reflects a linear model:

\[x\] 2 4 6 8 10
\[y\] 8 2 -8 -18 -24
  1. Construct the linear regression model \(\hat{y}={{b}_{0}}+{{b}_{1}}x\) that corresponds to this data. [ COMMENTS & HINTS: Use a calculator or spreadsheet to determine the least squares equation or line of best fit; a computational table is not necessary.]
  2. Determine the Pearson product moment correlation coefficient, r . [ COMMENTS & HINTS: Express the terminating decimal answer precisely, without rounding. Again, use technology to your advantage so to avoid tedious computations.]
  3. What percentage of the variability is due to the linear relationship between the two variables? [ COMMENTS & HINTS: Compute the coefficient of determination.]
  4. If \(x=5\), what is the predicted value for y ?
  5. What value for x corresponds to a predicted value \(\hat{y}=-22.7\) ?

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