Question

A random sample of records of sales of homes in a city gives the Price and Size​ (in square​ feet) of 117 homes. A regression to predict Price​ (in thousands of​ dollars) from Size has an Rsquared of 68.6​%. Write a sentence in context summarizing what the Rsquared says about this regression. Choose the correct answer below. A. A linear model on Price accounts for 68.6​% of the variation in home Size. B. A linear model on Price accounts for 31.4​% of the variation in home Size. C. A linear model on Size accounts for 82.8​% of the variation in home Price. D. A linear model on Size accounts for 31.4​% of the variation in home Price. E. A linear model on Price accounts for 82.8​% of the variation in home Size. F. A linear model on Size accounts for 68.6​% of the variation in home Price.

Answer 1

Answer:

F. A linear model on Size accounts for 68.6​% of the variation in home Price.

Explanation:

R-squared ($R^{2}$) is a statistical measure used in a regression model to describes the percentage or proportion of variance or variation in a dependent variable which is explained by or can be predicted from the independent variable of the model.

R-squared is also known the coefficient of determination.

In the question, the dependent variable is the price, while the independent variable is the size. That is why the aim is to determine the percentage or proportion of variance or variation of price of homes which is explained by or can be predicted from the size of homes.

Given the R-squared of 68%, the correct answer is option F which states that "a linear model on Size accounts for 68.6​% of the variation in home Price". This implies that 68% variation in the price of home can be explained by or predicted from the size of home.

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