Concrete expands both horizontally and vertically over time. The article "Evaluation of the Expansion Attained to Date by Concrete Affected by AlkaliSilica Reaction. Part III: Application to Existing Structures" (M. Bérubé, N. Smaoui, et al., Canadian Journal of Civil Engineering, 2005:463-479) reports measurements of horizontal and vertical expansion (in units of parts per hundred thousand) made at several locations on a bridge in Quebec City in Canada. The results are presented in the following table.

a. Construct a scatterplot of vertical expansion (y) versus horizontal expansion \((x)\). Verify that a linear model is appropriate.

b. Compute the least-squares line for predicting vertical expansion \((y)\) from horizontal expansion \((x)\).

c. Compute the fitted value and residual for each point.

d. If the horizontal expansion is 10 parts per hundred thousand, what do you predict the vertical expansion to be?

e. Predict the vertical expansion for a location where the horizontal expansion is 30 parts per hundred thousand.

f. Can the least-squares line be used to predict the vertical expansion in a location where the horizontal expansion is 60 parts per hundred thousand? If so, predict the expansion. If not, explain why not.
g. For what horizontal expansion would you predict a vertical expansion of 65 parts per hundred thousand?

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Horizontal 43 5 18 24 32 10 21 Vertical 55 80 58 68 57 69 63