Question

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STAT 3038-001: Probability & Statistics II HW 2 4. (Exercise 3.8, 3.24, 3.40) Predicting home sales price. Real estate investors, homebuyers, and homeowners often use the appraised (or market value of a property as a basis for predicting sale price. Data on sale prices and total appraised values of 76 residential properties sold in 2008 in an upscale Tampa, Florida, neighborhood named Tampa Palms are saved in "TAMPALMS.txt" file. The following scatter plot and regression result are produced by R. Scatterplot of Sale_Price vs Market_Var 1500 Sale_Price 1000 500 200 400 1000 1200 600 800 Market_Val Call: lm (formula = Sale_Price - Market_val) Coefficients: Estimate Std. Error t value Pr>t) (Intercept) 1.35868 13.76817 0.099 0.922 Market_Val 1.40827 0.03693 38.132 <2e-16 *** Signif. codes: O'***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1'' 1 Residual standard error: 68.76 on 74 degrees of freedom Multiple R-squared: 0.9516, Adjusted R-squared: 0.9509 F-statistic: 1454 on 1 and 74 DF, p-value: < 2.2e-16 (a) Propose a straight-line model to relate the appraised property value to the sale price y for residential properties in this neighborhood. (Note: Here, you just need to write a general form of the regression model using y and 21, not the specific values from data. The 'fitted line" will be answered in part (c) below) (1 pt) (b) The R scatter plot of the data is shown above. [Note: Both sale price and total market value are shown in thousands of dollars. Does it appear that a straight-line model will be an appropriate fit to the data? (1 pt)

This is should be the

TAMPALMS.txt (1.292 KB)

Property   Market_Val   Sale_Price
1   181.44   382.0
2   191.00   230.0
3   159.83   220.0
4   189.22   277.0
5   151.61   205.0
6   166.40   250.0
7   157.09   235.0
8   211.74   284.0
9   146.45   247.7
10   131.80   159.0
11   131.05   200.0
12   191.98   285.0
13   138.85   170.0
14   147.95   215.0
15   121.98   149.0
16   113.08   165.0
17   138.02   205.0
18   162.65   262.5
19   177.44   250.0
20   163.30   280.0
21   279.67   335.0
22   358.81   580.0
23   192.83   275.0
24   203.91   310.0
25   298.71   310.0
26   319.03   290.0
27   213.37   268.0
28   219.52   311.5
29   219.52   311.5
30   240.91   350.0
31   168.48   300.0
32   165.53   236.0
33   171.04   210.0
34   164.48   275.0
35   352.70   550.0
36   373.10   525.0
37   261.84   300.0
38   160.27   270.0
39   1262.27   1600.0
40   784.36   1225.0
41   676.70   1040.0
42   810.08   860.0
43   244.92   334.0
44   279.57   449.0
45   277.20   408.0
46   345.11   455.0
47   367.15   525.0
48   341.75   430.0
49   332.14   455.0
50   190.43   300.0
51   213.22   300.0
52   208.76   350.0
53   1072.13   1700.0
54   279.72   450.0
55   520.59   850.0
56   537.33   780.0
57   296.30   435.0
58   312.16   400.0
59   268.23   340.0
60   710.14   1000.0
61   599.19   862.0
62   762.98   1200.0
63   330.37   460.0
64   306.20   448.0
65   446.70   660.0
66   508.77   800.0
67   161.15   210.0
68   199.44   295.0
69   270.51   300.0
70   238.79   337.5
71   207.11   270.0
72   263.40   325.0
73   194.58   252.0
74   219.15   270.0
75   322.67   305.0
76   325.96   450.0

Answer 1

1. This simple linear regression calculator uses the least squares method to find the line of best fit for a set of paired data, allowing you to estimate the value of a dependent variable (Y) from a given independent variable (X).

The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X = 0). This calculator will determine the values of b and a for a set of data comprising two variables, and estimate the value of Y for any specified value of X.

2. Yes, the liner fit is the best fit for this data, because there is linear pattern exists in the scatter plot.

3. Sale Price= 1.35868 + 1.40827* Market value; from the estimate column.

4. If effect of the market value is zero, then then the price will be 1.35868. this interpretation of the intercept.

5. Slope, if the market value is changes by 1 unit then the sale price will change by the 1.40827 units.

6. X=300 then y=?

Sale Price= 1.35868 + 1.40827* 300

Y = 423.84

7. Yes, there is significant contribution of the beta in the model, because the beta has a significant p-value (2.2e-16), which is less than the 0.01.

8. Coefficient of determination = R²=0.9516, in percentage it would be a 95.16% variation is explained by the market value to predict the sale price.

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