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

The correct interpretation of an R-squared value of 68.6% in the context of a regression analysis for home prices and size is that the size of the home accounts for 68.6% of the variation in the home prices.

Step-by-step explanation:

The student has provided data from a regression analysis that was conducted to predict home prices from the size of homes in square feet. The R-squared value given is 68.6%, which is a key statistic in regression analysis. This value can be interpreted as follows: a linear model on size accounts for 68.6% of the variation in home prices. This means that over two-thirds of the changes in home prices can be explained by the changes in the size of the homes, according to the model.

Therefore, the correct answer is F: A linear model on Size accounts for 68.6% of the variation in home Price.

Answer 2

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

Step-by-step 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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