We repeat the information. Presuming that the assumptions for regression inferences are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for predicting the response variable.

Following are the data on the percentage of investments in energy securities and tax efficiency from Exercise 14.22. Use α = 0.05.

 Exercise 14.22

Tax efficiency is a measure ranging from 0 to 100, of how much tax due to capital gains stock or mutual funds investors pay on their investments each year; the higher the tax efficiency, the lower is the tax. The paper “At the Mercy of the Manager” by C. Israelsen examined the relationship between investments in mutual fund portfolios and their associated tax efficiencies. The following table shows the percentage of investments in energy securities (x) and tax efficiency (y) for 10 mutual fund portfolios.

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x y 3.1 3.2 3.7 4.3 4.0 5.5 6.7 7.4 7.4 10.6 98.1 94.7 92.0 89.8 87.5 85.0 82.0 77.8 72.1 53.5