Question

A sample of 30 recently sold single-family houses in a small city is selected. Develop a model to predict the selling price (in thousands of dollars), using the assessed value (in thousands of dollars) as well as time (in months since reassessment). The houses in the city had been reassessed at full value one year prior to the study. The results are stored in House1.xls.

a. State the multiple regression equation.

b. Interpret the meaning of the slopes in this equation.

c. Predict the selling price for a house that has an assessed value of $170,000 and was sold 12 months after reassessment.

d. Perform a residual analysis on your results and deter-mine whether the regression assumptions are valid.

e. Determine whether there is a significant relationship be-tween selling price and the two independent variables (assessed value and time period) at the 0.05 level of significance.

f. Determine the p-value in (e) and interpret its meaning.

g. Interpret the meaning of the coefficient of multiple determination in this problem.

h. Determine the adjusted

i. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.

j. Determine the p-values in (i) and interpret their meaning.

k. Construct a 95% confidence interval estimate of the population slope between selling price and assessed value.

EXCEL DATA BELOW:

Price($000)	Assessed Value	Type	Time
194.10	178.17	0	10
201.90	180.24	0	10
188.65	174.03	1	11
215.50	186.31	1	2
187.50	175.22	1	5
172.00	165.54	1	4
191.50	172.43	1	17
213.90	185.61	1	13
169.34	160.80	1	6
196.90	181.88	0	5
196.00	179.11	1	7
161.90	159.93	1	4
193.00	175.27	1	11
209.50	185.88	0	10
193.75	176.64	1	17
206.70	184.36	1	12
181.50	172.94	1	5
194.50	176.50	0	14
169.00	166.28	1	1
196.90	179.74	0	3
186.50	172.78	1	14
197.90	177.90	0	12
183.00	174.31	1	11
197.30	179.85	0	12
200.80	184.78	0	2
197.90	181.61	0	6
190.50	174.92	1	12
197.00	179.98	0	4
192.00	177.96	1	9
195.90	179.07	0	12

This question was asked, and partially answered once before. However, I need step by step answers to for a clearer comprehension. Please provide answers for a through k

Answer 1

Using Minitab software, (Stat -> Regression -> Regression -> Fit Regression Model), we get the following output :

a) The multiple regression equation is

Price = -120.0 + 1.7506*Assessed Value + 0.368*Time

b) Interpretation of slope -

For a unit increase in the Assessed value, Price will increase by 1750.6 dollars.

If number of months after reassessment increases by one unit, price will increase by 368 dollars.

c) The predicted selling price for a house that has an assessed value of $170,000 and was sold 12 months after reassessment

= -120.0 + (1.7506*170) + (0.368*12)

= 182.018

d)

Since histogram of residuals is not skewed, we can say that the regression assumptions are not valid.

e) The value of test statistic F = 223.46

f) P-value = 0

Since P-value = 0 < 0.05, so at 5% level of significance we can conclude that regression model is significant.

g) coefficient of determination = R² = 94.30%

94.30% variation in price can be explained by the regression equation.

h) adjusted R² = 93.88%

i) Testing the significance of Assessed value,

The value of t test statistic = 20.41 which follows a t distribution with df = 27

P-value = 0

Testing the significance of Time,

The value of t test statistic = 2.87 which follows a t distribution with df = 27

P-value = 0.008

j) Testing the significance of Assessed value,

Since P-value = 0 < 0.05, so at 5% level of significance we reject the null hypothesis and we can conclude that assessed value has a significant effect on price.

Testing the significance of Time,

Since P-value = 0.008 < 0.05, so at 5% level of significance we reject the null hypothesis and we can conclude that time has a significant effect on price.

k) Here,

slope

standard error of slope

and sample size

a 95% confidence interval estimate of the population slope between selling price and assessed value