A real estate association in a suburban community would like to study the relati

Question

A real estate association in a suburban community would like to study the relationship between the size of a single-family house (as measured by the number of rooms) and the selling price of the house (in thousands of dollars). Two different neighborhoods are included in the study, one on the east side of the community

(equals=0)

and the other on the west side

(equals=1).

A random sample of 20 houses was selected, with the results given below. Complete parts (a) through (g). For parts (a) through (d), do not include an interaction term.

Upper X 1X1,

Upper X 2X2.

ModifyingAbove Upper Y with caret Subscript iYiequals=nothing plus+(nothing )Upper X Subscript 1 iX1iplus+(nothing )Upper X Subscript 2 iX2i

(Round to three decimal places as needed. Do not include the $ symbol in your answers.)

Interpret the regression coefficients in (a).

At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model.

Construct and interpret a 95% confidence interval estimate of the population slope of the relationship between selling price and number of rooms.

Price Rooms Neighborhood 309.6 7 0 307.4 8 0 350.3 10 0 346.5 12 0 298.2 6 0 337.8 9 0 324.2 10 0 313.2 8 0 328.1 9 0 325.4 8 0 297.2 6 0 383.4 13 1 339.2 10 1 338.3 9 1 344.3 9 1 325.8 8 1 341.7 9 1 345.5 9 1 362.6 11 1 350.1 9 1 State the multiple regression equation that predicts the selling price, based on the number of rooms,

Upper X 1X1,

and the neighborhood,

Upper X 2X2.

ModifyingAbove Upper Y with caret Subscript iYiequals=nothing plus+(nothing )Upper X Subscript 1 iX1iplus+(nothing )Upper X Subscript 2 iX2i

(Round to three decimal places as needed. Do not include the $ symbol in your answers.)

Interpret the regression coefficients in (a).

At the 0.05 level of significance, determine whether each independent variable makes a contribution to the regression model.

Construct and interpret a 95% confidence interval estimate of the population slope of the relationship between selling price and number of rooms.

Explanation / Answer

A)

price^ = b0 + b1 * X1 + b2 *X2

X1 = rooms , X2 = dummy variable for neighbourhood

we get

price^ = 242.0777 + 9.409 * room + 14.846 * neighborhood

p-value < 0.05 , the variable is significant

here p-value of both room and neighborhood < 0.05

hence both variable are significant

95% confidence estimate of the population slope of the relationship between selling price and number of rooms. (b1)

= (7.100646, 11.7175)

SUMMARY OUTPUT Regression Statistics Multiple R 0.940451126 R Square 0.884448321 Adjusted R Square 0.870854006 Standard Error 7.792802031 Observations 20 ANOVA df SS MS F Significance F Regression 2 7901.916021 3950.95801 65.06016002 1.08043E-08 Residual 17 1032.371979 60.72776349 Total 19 8934.288 Coefficients Standard Error t Stat P-value Lower 95% Intercept 242.0777778 9.544194321 25.36387773 5.97395E-15 221.9412879 Rooms 9.409080048 1.094139978 8.599521303 1.34606E-07 7.100646478 Neighborhood 14.84555954 3.745279935 3.963805055 0.001002868 6.943709587

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