MTH 305 | Assignment 3 | Complete Solution
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Assignment 3
Possible Total Points: 60 pts
Instructions:
- Turn in your answers in paper-form (hand-written or typed) by the beginning of class.
- Include complete sentences and show all calculations.
- Each question is equally weighted.
- Partial credit is possible even if an answer is incomplete.
EXERCISE #1. Ch. 13 (section 13.2): Problem #13.1 (p. 523)
- Fitting a straight line to set a data yields the ff prediction line
Yi=2+5Xi
- Interpret the meaning of the Y intercept b0.
- Interpret the meaning of the slope b1
- Predict the mean value of Y for X=3
EXERCISE #2. Ch. 13 (section 13.2): Problem #13.9 all except part (a) (p. 525)
An agent for residential real estate company in a large city would like to be able to predict the monthly rental cost for apartments based on the size of the apartment as defined by square footage. A sample of 25 apartment RENT in a particular residential neighborhood was selected, and the information gathered revealed the following
Apartment Monthly Rent ($) Size ( Square Feet) Apartment Monthly Rent Size
1 950 850 14 1,800 1,369
2 1,600 1,450 15 1,400 1,175
3 1,200 1,085 16 1,450 1,225
4 1,500 1,232 17 1,100 1,245
5 950 718 18 1,700 1,259
6 1,700 1,485 19 1,200 1,150
7 1,650 1,136 20 1,150 896
8 935 726 21 1,600 1,361
9 875 700 22 1,650 1,040
10 1,150 956 23 1,200 755
11 1,400 1,100 24 800 1,000
12 1,650 1,285 25 1,750 1,200
13 2300 1,985
14 1,800 1,369
15 1,400 1,175
b) Use the least –squares method to find the regression coefficients b0 and b1.
c) Interpret the meaning of b0 and b1 in this problem.
d) Predict the mean monthly rent for an apt. that has 1,000 square feet.
e) Why would it not be appropriate to use the model to predict the monthly rent for apts. That have 500 square feet?
f) Your friend Jim and Jennifer are considering signing a lease for an apt. in this residential neighborhood. They are trying to decide between two apts, one with 1,000 square feet for a monthly rent of 1,275 and the other with 1,200 square feet for a monthly rent of 1,425. What would you recommend to them? Why?
For part (b): Below is the dataset you need to solve this problem in Excel. To get the intercept b0 and slope b1, you can use the “Regression Analysis” function in Excel or type these commands in any Excel cell:
=SLOPE(range of Y data, range of X data)
=INTERCEPT(range of Y data, range of X data)
Rent
Size
950
850
1600
1450
1200
1085
1500
1232
950
718
1700
1485
1650
1136
935
726
875
700
1150
956
1400
1100
1650
1285
2300
1985
1800
1369
1400
1175
1450
1225
1100
1245
1700
1259
1200
1150
1150
896
1600
1361
1650
1040
1200
755
800
1000
1750
1200
EXERCISE #3. Ch. 13 (section 13.3): Problem #13.21 (p. 531)
In problem 13.9 on page 255 an agent for real estate company wanted to predict the monthly rent for apts. Based on the size of the apt. Rent using of the apt, RENT using the results of that problem.
- Determine the coefficient of the determination r^2 and interpret its meaning.
- Determine the standard error of the estimate.
- How useful do you thing this regression model is for predicting the monthly year?
For parts (a) and (b): To get the intercept r2 and the standard error you can use the output from the “Regression Analysis” function you got for Problem #13.19 above (see Exercise #2), or type these commands in any Excel cell:
=RSQ(range of Y data, range of X data)
=STEYX(range of Y data, range of X data)
EXERCISE #4. Ch. 14 (section 14.6): Problem #14.38 (p. 600)
Suppose X1 is a numerical variable and X2 is a dummy variable and the following regression equation for a sample n= 20 is: Y1 = 6+4 x 1i + 2X 2i
- Interpret the meaning of the slope for variable X1.
- Interpret the meaning of the slope for variable X2
- Suppose that the t statistic for testing the contribution of variable X2 is 3.27. At the 0.05 level of significance, is there evidence that variable X2 makes a significant contribution to the model?
EXERCISES #5 & 6. Ch 14: Problem #14.72 all part except (d) and (i) (p. 613)
The file AUTO2002 contains data on 121 automobile models from the year 2002. Among the variables included are the gasoline mileage ( in miles per gallon), the length ( in inches), and the weight (in pounds) of each automobile. Develop a model to predict the gasoline mileage based on the length and weight of each automobile.
- State the multiple regression equation.
- Interpret the meaning of the slopes in this equation.
- Predict the gasoline mileage for an automobile for an automobile that has the length of 195 inches and weight of 3,000 pounds.
e )Is there a significant relationship between gasoline mileage and the two independent variables (length and weight) at the 0.5 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 r2.
j) Determine the p-value in (i) and interpret their meaning. ( (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).
k) Construct a 95% confidence interval estimate of the population slope between gfasoline mileage and weight.
l) Compute and interpret the coefficients of partial determination.
The Excel output for this exercise is given below. Use this output to answer the questions.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.782187748
R Square
0.611817673
Adjusted R Square
0.60186428
Standard Error
2.952425134
Observations
121
ANOVA
df
SS
MS
F
Significance F
Regression
3
1607.421998
535.8073326
61.46825227
6.20871E-24
Residual
117
1019.867258
8.716814173
Total
120
2627.289256
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
42.43290086
8.218578926
5.163045977
1.00728E-06
26.15643651
58.70936521
Length
-0.00667189
0.036217633
-0.18421688
0.854162226
-0.07839902
0.065055222
Width
-0.03989444
0.182924039
-0.21809293
0.827736634
-0.40216590
0.322377022
Weight
-0.00487697
0.000600754
-8.11807648
5.3858E-13
-0.00606673
-0.00368720
[Solved] MTH 305 | Assignment 3 | Complete Solution
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The predicted monthly rent when the size of the apartment is 1,000 square feet is,
Monthly Rentest = 177.12 + 1.065 (1,000) = 177.12 + 1,065 = 1,242.12.
MTH 305 | Midterm Exam | Complete Solution
Null Hypothesis: the amount of soft drink in a bottle at a soft drink plant averages 2 liters. That is u = 2
Alternative Hypothesis: the amount of soft drink in a bottle at a soft drink plant does not average 2 liters...
MTH 305 | Assignment 3 | Complete Solution
The predicted monthly rent when the size of the apartment is 1,000 square feet is,
Monthly Rentest = 177.12 + 1.065 (1,000) = 177.12 + 1,065 = 1,242.12.
The predicted monthly rent when the size of the apartment i...