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A group of twenty homes in a subdivision have sold in the past year. They ranged in size from 4000 to 7000 square feet, with an average size of 5000 square feet and a standard deviation of 600 square feet. The average selling price was $1,000,000 with a standard deviation of $100,000. The correlation between home size and selling price is [tex]r_{xy} = 0.9000[/tex].

You want to fit a linear model to this data to estimate the response variable, selling price, using house size as the explanatory variable. Use this information to answer questions 9 through 13.

Should this model be used to predict the value of a home of 6950 square feet in area?

A. Yes, the value is $1,292,500.00.
B. Yes, the value is $1,562,650.00.
C. No, you must know the value of de Krums T to calculate the value.
D. No, 6950 sq. ft is outside the range of the data.

Answer :

Yes, this model can be used to predict the value of a home of 6950 square feet in area. The estimated selling price using the linear model would be $1,241,670.

Yes, this model can be used to predict the value of a home of 6950 square feet in area. The linear model utilizes the correlation between home size and selling price (rxy = 0.9000) to estimate the response variable, selling price, using house size as the explanatory variable. By plugging the given home size (6950 square feet) into the linear model, we can calculate the estimated selling price.

The estimated selling price, we first calculate the z-score for the home size based on the mean and standard deviation. The formula for the z-score is: z = (x - mean) / standard deviation. So, the z-score for a home size of 6950 square feet would be: (6950 - 5000) / 600 = 2.4167.

Next, we can use the formula for the estimated selling price: estimated selling price = mean selling price + (z-score * standard deviation selling price). Plugging in the values, we get: estimated selling price = $1,000,000 + (2.4167 * $100,000) = $1,241,670. Therefore, the estimated value of a home with an area of 6950 square feet would be $1,241,670.

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