United Park City Properties real estate investment firm took a random sample of five condominium units that recently sold in the city. The sales prices Y (in thousands of dollars) and the areas X (in hundreds of square feet) for each unit are as follows Y= Sales Price ( * $1000) 36 80 44 55 35 X = Area (square feet) (*100) 9 15 10 11 10 The owner wants to forecast sales on the basis of the area. Which variable is the dependent variable? Which variable is the independent variable? Determine the regression equation. Interpret the values of the slope and the intercept. Test the significance of the slope at 1% level of significance. Determine the coefficient of correlation between the sales price and the area. Interpret the strength of the correlation coefficient. Determine the coefficient of determination and present its interpretation. Determine the coefficient of non-determination. SUMMARY OUTPUT Regression Statistics Multiple R 0.969217713 R Square 0.939382976 Adjusted R Square 0.919177301 Standard Error 5.284339356 Observations 5 ANOVA df SS MS F Significance F Regression 1 1298.227 1298.227 46.49105 0.006453 Residual 3 83.77273 27.92424 Total 4 1382 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -34.5 12.61619 -2.73458 0.071664 -74.6503 5.650339 -74.6503 5.650339 Area 7.681818182 1.126625 6.818434 0.006453 4.096395 11.26724 4.096395 11.26724
Added by Adriana W.
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The dependent variable is the sales price (Y) because it is the variable we are trying to predict or forecast. The independent variable is the area (X) because it is the variable we are using to make the prediction. Show more…
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A real estate expert wanted to find the relationship between the sale price of houses and various characteristics of the houses. She collected data on five variables for 25 houses that were sold recently. Dependent variable is the sale price of the house (in 1000 TL). Independent variable X1 refers to size of the house in sq.meters, X2 refers to size of the living area in sq.meters, X3 refers to age of the house in years, X4 refers to number of rooms in the house, and X5 refers to whether the house has a private garage (X5 = 1 if the answer is yes, X5 = 0 if the answer is no). The following regression output (with some values missing, you have to fill them as much as you can) was presented to the real estate expert: Regression Statistics Multiple R 0.907 R Square Adjusted R Square Standard Error Observations 25 ANOVA SS df MS F p-value Regression 417 Residual/Error 89 Total 506 Coefficients Standard Error t stat p-value Intercept 200.15 5.6128 X1 11.90 0.456 X2 0.10 0.087 X3 -7.55 0.239 X4 19.00 10.00 X5 8.50 0.042 The following correlation matrix was developed. Based on this, which variable(s) indicate(s) a multicollinearity problem? X1 X2 X3 X4 X5 X1 1 X2 -0.539 1 X3 -0.953 0.885 1 X4 0.008 0.235 0.930 1 X5 0.252 0.456 -0.860 0.332 1 Select one: a. X4 b. X2 c. X3 d. X2 and X3 e. X2, X3, and X5 f. X5 g. X1 h. X3 and X4 i. X1 and X3
Aishwarya K.
Correlation and Regression. This data contains attributes of a random sample of 25 apartment buildings in a city in Minnesota. The price of the apartment building is the dependent variable. Price is expressed in $1,000s (divide PRICE by 1,000). PRICE is thought to be a function of the following independent variables: #APTS - The number of apartments in the building AGE - The age of the apartment building in years LOTSIZE - The lot size that the building is on in square feet PARKING - The number of parking spaces AREA - The total area in square footage EXCDum - This is a dummy variable of the condition of the building. 1 = Excellent Condition and 0 is not Excellent The Correlation Matrix is given below. PRICE #APTS AGE LOTSIZE PARKING AREA EXCDum 1.0000 0.9235 -0.1145 0.7418 0.2249 0.9681 0.1618 1.0000 -0.0142 0.7997 0.2241 0.8779 -0.0833 1.0000 -0.1909 -0.3627 0.0270 0.1531 1.0000 0.1669 0.6728 -0.2019 1.0000 0.0893 -0.1767 1.0000 0.1992 1.0000 Suppose we regress PRICE on #APTS and we generate the following equation: Estimated PRICE = 101.7862 + 15.5253*#APTS The R-square from this Regression would be:
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In the context of linear regression, the standard error tells us the proportion of total variation in the dependent variable that can be explained by the independent variable. ( ) True ( ) False A real estate agent claimed that the mean price for homes in Annandale city is $400,000. A student in STAT 1051 believed that the mean price is higher. To test the agent's claim, the student selected a random sample of 100 homes in the city and calculated the mean and standard deviation for the 100 homes, which are $420,000 and $65,000, respectively. The formulated set of hypotheses will be: A 95% confidence interval for the difference between two population means is (-2.765, 8.162). Based on this 95% confidence interval, one can conclude that the mean of population 1 is less than the mean of population 2 by 2.765. ( ) True ( ) False Suppose an appliance store conducts a 12-month experiment to determine the effect of advertising on sales revenue. The store used a simple linear regression where the independent variable X (in hundreds of dollars) is advertising expenditure and the dependent variable Y (in thousands of dollars) is sales revenue. The results are shown below. SUMMARY OUTPUT Regression Statistics Multiple R: 0.946 R-square: 0.896 Adjusted R Square: 0.886 Standard error: 0.978 Observations: 12 ANOVA df: SS: MS: F-test: Significance F: Regression 1 83.084 83.084 86.701 0.00000034 Residual 10 9.583 0.958 Total 11 92.667 Coefficient Standard error t-stat P-value Lower 95% Upper 95% Intercept -0.621 0.603 -1.031 0.023 -1.963 0.721 Sales revenue 0.762 0.082 9.311 0.00000034 0.579 0.945 According to this model, how much sales revenue, on average, when the advertising cost is 10,000? Note: advertising cost is in hundreds of dollars and sales are in thousands of dollars. ( ) a. 75.616 thousands ( ) b. 77.205 thousands ( ) c. 73.764 thousands ( ) d. none of the above
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