Set 1 (Old Faithful\'s Time Between Eruptions and Length of Eruption) Length = -

Question

Set 1 (Old Faithful's Time Between Eruptions and Length of Eruption)

Length = - 0.378 + 0.185 Time, R-Sq = 83.0%

Set 2 (In high-fiber cereals, Number of Calories and Number of Grams of Sugar)

Calories = 183 + 0.829 Sugar, R-Sq = 6.8%

Set 3 (Per Capita Disposable Income and Per Capita Consumption)

Consumption = - 7586 + 1.31 Income, R-Sq = 99.0%

For which set is the linear regression model most adequate for describing the relationship between two variables?  (On a related note, we would expect this model to provide the most accurate predictions/estimates.)  Explain. For which set does linear regression appear to be inappropriate?  That is, the linear regression model does not do a good job explaining the relationship between the two variables.  Explain.

Explanation / Answer

1) Out of three models, Consumption = - 7586 + 1.31 Income, R-Sq = 99.0% is the most adequate for describing the relationship between two variables.

i.e. 99% of the variation in the dependent variable(consumption) is explained by only the income. And also there is high positive correlation between income and consumption.

2) Out of three models, Calories = 183 + 0.829 Sugar, R-Sq = 6.8% is an inappropriate model.

Here only 6.8% of the variation in the dependent variable only explained by the sugar and also there is a low positive correlation between sugar and calories.

Therefore Set2 is an inappropriate.

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