The following data represent the living area x in 100 square

The following data represent the living area x (in 100 square ft), and the selling price Y (in $100) for a sample of 15 houses from a new subdivision in a town. For example, the selling price of the house 1 with 2,790 ft^2 is $457,200. For these data, x = 25.74. and (n - 1)sx^2 = 41.06. Construct a scatter plot and explain the relationship between Y and X. Write the fitted model and the value of r^2. On the basis of r^2, can we say that the model is well fitted? Explain. interpret the meanings of b in the context of the problem. Predict the selling price of a house in the neighborhood with the living area of 2,700 squareroot feet (i.e., x^* = 27). By comparing the above predicted price (in part e) with the prices of the House 3 (2,750 ft^2) and House 15 (2.666 ft^2), can we say that the predicted price is reasonable? Explain. Find a 95% prediction interval of a house in the neighborhood with the living area of 2,700 squareroot feet. Find, 95% confidence interval for the mean price of all houses in the subdivision with the living area of 2,700 ft^2 and interpret its meanings. Y^ = a + bx^ , PI: Y^ plusminus tn-2; 1-a/2Se squareroot 1 + 1/n + (x^ - x)^2/(n - 1)Sx^2; CI: Y^ plusminus tn-2; 1-a/2Se squareroot 1 + 1/n + (x^ - x)^2/(n - 1)Sx^2

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