Question
In: Statistics and Probability
The following table illustrates the “Multiple Regression” output for “Selling Price” regressed on two independent (predictor)...
The following table illustrates the “Multiple Regression” output for “Selling Price” regressed on two independent (predictor) variables. Given the output, evaluate the significance, if any, of the individual independent variables at the 5% significance level. Make sure that you provide your rationale for your response for each independent variable. Also, indicate what the appropriate regression equation is for estimating the selling price
| Regression Statistics | ||||
| Multiple R | 0.81968 | |||
| R Square | 0.67188 | |||
| Anova | DF | SS | MS | F |
| Regression | 2 | 13313936968 | 6.7E+09 | 11.2619 |
| Residual | 11 | 6502131603 | 5.9E+08 | |
| Total | 13 | 19816068571 | ||
| Coefficient | Standard Error | t-Stat | p-value | |
| Intercept | 146631 | 25482.0829 | 5.7543 | 0.0001 |
| Square Feet | 43.8194 | 10.2810 | 4.2622 | 0.0013 |
| Age | -2898.69 | 796.5649 | -3.6390 | 0.0039 |
Solutions
Expert Solution
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Based on the output in the table, here' the evaluation:
Variables with p-value < .05 ( 5% significance threshold given in the question), will be statistically significant.
Since, Age and Square Feet have p-values of .0039 and .0013 respectively, they are less than .05
Therefore, both have a significant linear relation with Selling Price.
Also, the R-square of .67199 means that the 67% of variation in Selling Price is explained by the independent variables. This is a moderately strong RSquare.
At an overall level, the linear regression is statistically significant.
The appropriate equation is : Selling Price^ = 146631 + 43.8194*SquareFeet - 2898.69*Age
Interpretation of each variable:
Square Feet: Per square feet increase in area of the house the house becomes expensive by 43.8194 units
This is as expected, as more the area more is the cost of the house
Age: As house ages by each year, the Selling price comes down by $2898.69
This is as expected, more the age of the house, more the wear-tear of the house, less will be the cost of the house, which justified the -ive coefficient of this variable
orchestra answered 1 year agoRelated Solutions
The final part of the multiple regression output is the coefficients table that represents the following:...
The final part of the multiple regression output is the
coefficients table that represents the following:
The unstandardized regression coefficient (B).
The standardized regression coefficient (beta or
β).
t and p values.
All the above.
Three correlation coefficients are displayed in the
coefficients table. They include the following:
The zero order correlation coefficient.
The partial correlation coefficient.
The part correlation coefficient.
All of the above.
If the value for tolerance is acceptable, one should proceed
with interpreting the:
Model summary....
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT Regression...
The following is the estimation results for a multiple linear
regression model:
SUMMARY OUTPUT
Regression Statistics
R-Square
0.558
Regression Standard Error
(S)
863.100
Observations
35
Coeff
StdError
t-Stat
Intercept
1283.000
352.000
3.65
X1
25.228
8.631
X2
0.861
0.372
Questions:
Interpret each coefficient.
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT Regression...
The following is the estimation results for a multiple linear
regression model:
SUMMARY OUTPUT
Regression Statistics
R-Square
0.558
Regression Standard Error
(S)
863.100
Observations
35
Coeff
StdError
t-Stat
Intercept
1283.000
352.000
3.65
X1
25.228
8.631
X2
0.861
0.372
Question:
1.
A. Write the fitted regression equation.
B. Write the estimated intercepts and slopes, associated with
their corresponding standard errors.
C. Interpret each coefficient.
1. Following R output is from fitting multiple regression of House price (Y) in thousand based...
1.
Following R output is from fitting multiple regression of House
price (Y) in thousand based on Finish Area(X1), Age(X2) and
Bedroom(X3).
Coefficients:
Estimate Std. Error t value
Pr(>|t|)
(Intercept) 190.11 2.587 73.48 0.00866
**
X1 2.30 0.010 228.00 0.00279 **
X2 -2.46 0.064 -38.03 0 .01674 *
X3 36.67 0.359 101.96 0.00624 **
-----------------------------
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1
‘ ’ 1
Residual standard error: 0.9204 on 1 degrees of
freedom
Multiple R-squared:...
Use the following multiple regression table to answer the following questions: Daily Demand High Temperature Price...
Use the following multiple regression table to answer the
following questions:
Daily Demand
High Temperature
Price
Day
144
73
$ 1.00
1
90
64
$ 1.00
0
0 = Weekend
108
73
$ 1.00
1
1 = Weekday
120
82
$ 1.00
1
54
45
$ 1.20
0
69
54
$ 1.20
1
126
86
$ 1.20
1
99
70
$ 1.20
0
48
73
$ 1.50
0
33
66
$ 1.50
0
90
75
$ 1.50
1
81
61...
DEFINE THE COMPONENTS OF A GENERAL MULTIPLE REGRESSION EQUATION. IN A MULTIPLE REGRESSION ANOVA TABLE, THE...
DEFINE THE COMPONENTS OF A GENERAL MULTIPLE REGRESSION
EQUATION.
IN A MULTIPLE REGRESSION ANOVA TABLE, THE DEGREES OF FREDOM FOR
THE REGRESSION IS EQUAL TO:
THE TEST TO CONFIRM WHETHER THE DEPENDENT VARIABLE CAN BE
ESTIMATED WITHOUT RELYING ON THE INDEPENDENT VARIABLES IS REFERRED
TO AS:
WHAT STATISITIC WOULD WE USE FOR TESTING TO SEE IF AT LEAST ONE
INDEPENDENT REGRESSION COEFFICIENTS IS SIGNIFICANT?
TO TEST INDEPENDENT VARIABLES INDIVIDUALLY TO DETERMINE WHETHER
THE REGRESSION COEFFICIENTS DIFFER FROM ZERO WOULD BE:...
DEFINE THE COMPONENTS OF A GENERAL MULTIPLE REGRESSION EQUATION. IN A MULTIPLE REGRESSION ANOVA TABLE, THE...
DEFINE THE COMPONENTS OF A GENERAL MULTIPLE REGRESSION
EQUATION.
IN A MULTIPLE REGRESSION ANOVA TABLE, THE DEGREES OF FREDOM FOR THE
REGRESSION IS EQUAL TO:
THE TEST TO CONFIRM WHETHER THE DEPENDENT VARIABLE CAN BE ESTIMATED
WITHOUT RELYING ON THE INDEPENDENT VARIABLES IS REFERRED TO
AS:
WHAT STATISITIC WOULD WE USE FOR TESTING TO SEE IF AT LEAST ONE
INDEPENDENT REGRESSION COEFFICIENTS IS SIGNIFICANT?
TO TEST INDEPENDENT VARIABLES INDIVIDUALLY TO DETERMINE WHETHER THE
REGRESSION COEFFICIENTS DIFFER FROM ZERO WOULD BE:...
You are given the following output for a multiple regression based on a sample of size...
You are given the following output for a multiple regression
based on a sample of size n = 10
Predictions
Coefficients
Standard Error
Constant
-0.58762
x1
b1=1.510
0.351
x2
b2=-0.245
0.157
x3
b3=1.823
0.836
SSR=17.56; SSE=8.56
(a) Calculate a 90% confidence interval for β1. Provide a clear
interpretation of the interval.
(b) Which predictor variable(s) – x1, x2, x3 – should be kept in
the regression model and why, if testing at a 5% level of
significance? (use two-sided tests)...
1. Selling price and amount spent advertising were entered into a multiple regression to determine what...
1.
Selling price and amount spent advertising were entered into a
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for this value?
Select one:
A. Holding the amount spent on advertising constant, an increase
of $100 in the price of the Sony Bravia will decrease sales by
0.03%.
B. None of these.
C. For a given amount spent on...
1. How is the variance affected when you add a predictor to a multiple regression model?...
1. How is the variance affected when you add a predictor to a
multiple regression model?
2. Why does multiple-regression modeling require subject-matter
expertise?
3. Can overfitting occur in a model with a high coefficient of
determination value? What would that mean for that model?
4. What is the process of assessing a model’s capacity to make
accurate predictions?
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