Create a hypothesis test question and show all the steps to solve it. Example: You found the mean for each quantitative variable. So, one at a time, is there significant evidence that the population maintenance cost for buses is more than###? and Find the regression equation for the 2 variables and explain what it is you found. Create a hypothesis test question for price and Size.
record | Agent | Price | Size | Bedrooms | Baths | Pool (yes is 1) | Garage (Yes is 1) | Days | Township | Mortgage type | Years | FICO | Default (Yes is 1) |
1 | Marty | 206424 | 1820 | 2 | 1.5 | 1 | 1 | 33 | 2 | Fixed | 2 | 824 | 0 |
2 | Rose | 346150 | 3010 | 3 | 2 | 0 | 0 | 36 | 4 | Fixed | 9 | 820 | 0 |
3 | Carter | 372360 | 3210 | 4 | 3 | 0 | 1 | 21 | 2 | Fixed | 18 | 819 | 0 |
4 | Peterson | 310622 | 3330 | 3 | 2.5 | 1 | 0 | 26 | 3 | Fixed | 17 | 817 | 0 |
5 | Carter | 496100 | 4510 | 6 | 4.5 | 0 | 1 | 13 | 4 | Fixed | 17 | 816 | 0 |
6 | Peterson | 294086 | 3440 | 4 | 3 | 1 | 1 | 31 | 4 | Fixed | 19 | 813 | 0 |
7 | Carter | 228810 | 2630 | 4 | 2.5 | 0 | 1 | 39 | 4 | Adjustable | 10 | 813 | 0 |
8 | Isaacs | 384420 | 4470 | 5 | 3.5 | 0 | 1 | 26 | 2 | Fixed | 6 | 812 | 0 |
9 | Peterson | 416120 | 4040 | 5 | 3.5 | 0 | 1 | 26 | 4 | Fixed | 3 | 810 | 0 |
10 | Isaacs | 487494 | 4380 | 6 | 4 | 1 | 1 | 32 | 3 | Fixed | 6 | 808 | 0 |
11 | Rose | 448800 | 5280 | 6 | 4 | 0 | 1 | 35 | 4 | Fixed | 8 | 806 | 1 |
12 | Peterson | 388960 | 4420 | 4 | 3 | 0 | 1 | 50 | 2 | Adjustable | 9 | 805 | 1 |
13 | Marty | 335610 | 2970 | 3 | 2.5 | 0 | 1 | 25 | 3 | Adjustable | 9 | 801 | 1 |
14 | Rose | 276000 | 2300 | 2 | 1.5 | 0 | 0 | 34 | 1 | Fixed | 20 | 798 | 0 |
15 | Rose | 346421 | 2970 | 4 | 3 | 1 | 1 | 17 | 3 | Adjustable | 10 | 795 | 0 |
16 | Isaacs | 453913 | 3660 | 6 | 4 | 1 | 1 | 12 | 3 | Fixed | 18 | 792 | 0 |
17 | Carter | 376146 | 3290 | 5 | 3.5 | 1 | 1 | 28 | 2 | Adjustable | 9 | 792 | 1 |
18 | Peterson | 694430 | 5900 | 5 | 3.5 | 1 | 1 | 36 | 3 | Adjustable | 10 | 788 | 0 |
19 | Rose | 251269 | 2050 | 3 | 2 | 1 | 1 | 38 | 3 | Fixed | 16 | 786 | 0 |
20 | Rose | 547596 | 4920 | 6 | 4.5 | 1 | 1 | 37 | 5 | Fixed | 2 | 785 | 0 |
21 | Marty | 214910 | 1950 | 2 | 1.5 | 1 | 0 | 20 | 4 | Fixed | 6 | 784 | 0 |
22 | Rose | 188799 | 1950 | 2 | 1.5 | 1 | 0 | 52 | 1 | Fixed | 10 | 782 | 0 |
23 | Carter | 459950 | 4680 | 4 | 3 | 1 | 1 | 31 | 4 | Fixed | 8 | 781 | 0 |
24 | Isaacs | 264160 | 2540 | 3 | 2.5 | 0 | 1 | 40 | 1 | Fixed | 18 | 780 | 0 |
25 | Carter | 393557 | 3180 | 4 | 3 | 1 | 1 | 54 | 1 | Fixed | 20 | 776 | 0 |
26 | Isaacs | 478675 | 4660 | 5 | 3.5 | 1 | 1 | 26 | 5 | Adjustable | 9 | 773 | 0 |
27 | Carter | 384020 | 4220 | 5 | 3.5 | 0 | 1 | 23 | 4 | Adjustable | 9 | 772 | 1 |
28 | Marty | 313200 | 3600 | 4 | 3 | 0 | 1 | 31 | 3 | Fixed | 19 | 772 | 0 |
29 | Isaacs | 274482 | 2990 | 3 | 2 | 1 | 0 | 37 | 3 | Fixed | 5 | 769 | 0 |
30 | Marty | 167962 | 1920 | 2 | 1.5 | 1 | 1 | 31 | 5 | Fixed | 6 | 769 | 0 |
We will use R in this case to solve the hypothesis and regression problem.
Now, the mean of the price is 360048.2, we can find it using the following code:
> data = read.table(file = 'clipboard',sep = '\t',header=TRUE)
> mean(data$Price)
[1] 360048.2
Now, we will propose the following null and alternative hypothesis:
Note that the test is a right tailed test. We will use the following statistic:
Now, the standard deviation of the price is 1178732.5. Hence the observed statistic value becomes:
Now,the p-value in this case would be:
Hence, at 95% confidence level, we can say that we fail to reject the null hypothesis.
The following code is used for calculation:
> mean(data$Price)
[1] 360048.2
> sd(data$Price)
[1] 117832.5
> pt(0.459,29,lower.tail=FALSE)
[1] 0.324828
Now, we will analyze the regression between price and space. The analysis in R is given below:
> model = lm(Price~Size,data=data)
> summary(model)
Call:
lm(formula = Price ~ Size, data = data)
Residuals:
Min 1Q Median 3Q Max
-88801 -38584 3610 34405 95796
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 17838.578 29916.627 0.596 0.556
Size 98.440 8.221 11.975 1.57e-12 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 48470 on 28 degrees of freedom
Multiple R-squared: 0.8366, Adjusted R-squared: 0.8308
F-statistic: 143.4 on 1 and 28 DF, p-value: 1.566e-12
From the summary of the result, we can see that the linear regression equation between price and size is
and the t test for coefficient of Size returns a value lesser than 0.05. Hence, we can say that the slope is non zero. Also the R squared statistic implies that the regression model explains 83.66% of the variation in Price, thus making the model good enough
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