For many years, rubber powder has been used in asphalt cement to improve performance. The article “Experimental Study of Recycled Rubber-Filled High-Strength Concrete” (Mag. Concrete Res. 2009: 549–556) included a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data:

a. Verify that a scatterplot supports the assumption that the two variables are related via the simple linear regression model.
b. Obtain the equation of the least squares line, and interpret its slope.
c. Calculate and interpret the coefficient of determination.

d. Calculate and interpret an estimate of the error standard deviation σ in the simple linear regression model.
e. The largest x value in the sample considerably exceeds the other x values. What is the effect on the equation of the least squares line of deleting the corresponding observation?

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X У ра y 112.3 75.0 99.2 73.3 97.0 71.0 95.8 68.0 92.7 57.7 103.5 59.3 86.0 48.7 89.0 57.8 102.0 74.3 86.7 48.5