Question

1a.   Pick either your Redfin or Zillow data, and put it in this table.

Home#	Estimate	Sale price
1	367,846	335,000
2	314,085	295,000
3	327,343	350,000
4	270,548	260,000
5	153,270	142,500
6	133,920	106,500
7	230,040	225,000
8	1,429,459	1.35M
9	135,240	134,000
10	210,515	212,000
11	344,369	342,000
12	279,008	270,000
13	406,836	395,000
14	301,213	277,500
15	156,575	190,000

b.   We’re going to test whether the slope of the regression line is zero or non-zero. Write hypotheses with the appropriate symbols, and then write that hypothesis in words, specific to this situation.
c.   Perform the calculations using whatever tool you like best. Excel is convenient, or you can use a calculator, or a website like this. Please report the F-statistic and the p-value.
d.   Using your p-value, make a conclusion regarding your hypotheses from part b. Be sure to make your conclusion about this specific situation.
e.   Your p-value is probably very close to 0 so you rejected the null hypothesis. If you failed to reject H0, why would that be bad news for the website you picked?

2.   Look at this cool scatterplot I made:

a.   Describe in 1 – 2 sentences the overall trend of the dots in this plot.

b.   The correlation coefficient is -0.407. Adding a trendline to the plot gives us this:

Does it appear that there is a negative trend to these points, or does it look like they are just randomly-distributed dots?
c.   The regression output is:

	Coefficients	Standard Error	t Stat	P- Value
Intercept	16.69423038	0.848559849	19.67360393	1.28
X	-0.156150685	0.082709556	-1.887940057	0.07

Based on the p-value for x, would you say there is a statistically significant downward trend in these dots? Explain your answer in a complete sentence or two.

d.   Would you be surprised if I told you that these numbers are randomly generated independently, and have nothing to do with each other? Why or why not?

3.   Based on everything you’ve learned in this course, separating randomness from significant effects is (select one) Easy / Difficult.

Answer 1

(1)

(a) Regression output using Excel:

Regression Analysis
	r²	0.997	n	15
	r	0.998	k	1
	Std. Error	17554.724	Dep. Var.	Sale price
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,221,456,545,052.0100	1	1,221,456,545,052.0100	3963.60	1.52E-17
Residual	4,006,188,281.3206	13	308,168,329.3324
Total	1,225,462,733,333.3300	14
Regression output					confidence interval
variables	coefficients	std. error	t (df=13)	p-value	95% lower	95% upper	std. coeff.
Intercept	8,793.5376						0.000
Estimate	0.9392	0.0149	62.957	1.52E-17	0.9070	0.9714	0.998

(b) Ho: β = 0 and Ha: β ≠ 0

Ho: The slope coefficient for Estimate is 0 and Ha: The slope coefficient for estimate is not 0

(c) F statistic = 3963.60, p- value = 0

(d) Since the p- value < 0.05, we reject Ho, and conclude that the slope coefficient for Estimate is different from 0

(e) Not quite sure what they are asking here. If you clarify, I may be able to help!