## Transcribed Text

Statistical Methods for Research
1.
Discuss and describe the basics of regression; What are we trying to accomplish; How does
regression work
2.
Discuss the underlying assumptions of a simple linear regression model: multiple regression
model: and polynomial regression model.
3. Consider the below regression output. Note that some values have been erased. In order to solve
all parts of this problem, you may have to find all the missing values first.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9613
R Square
Adjusted R
Square
0.9222
Standard Error
Observations
200
ANOVA
Significance
df
SS
MS
F
F
Regression
479410417802.47
95882083560.49
0.00
Residual
202929702.05
Total
518778780000.00
Upper
Coefficients
Standard Error
Stat
P-value
Lower 95%
95%
Intercept
45482.366
19403.8863
2.34
0.0201
v1
-10383.543
3153.7202
-3.29
0.0012
v2
11.088
10.4859
1.06
0.2916
v3
738.388
175.8223
4.20
0.0000
v4
0.014
0.0023
6.37
0.0000
v5
-2.546
1.2209
-2.09
0.0383
a. Give the regression model from the table.
b. Determine the degrees of freedom (and fill in the blanks in the table).
c.
Find the Error Sum of Square (SSE) (and fill in the blank in the table).
d.
For testing the significance of overall regression find F-calc (and fill in the blank in the table).
Conduct the hypothesis test; Is regression significant.
e. Find the standard error for the data (and fill in the blank in the table).
1
Statistical Methods for Research
f.
Find the coefficient of determination, R-squared, (and fill in the blank in the table). Give an
interpretation of the value of R-squared.
g.
Find the 95% confidence intervals for all parameters; (and fill in the blanks in the table). Assume
that the critical t-value for a 95% confidence interval is 1.96 (from a t-table)
h. Conduct all parameter tests using alpha = 0.05 (5%).
Which parameters are significant; wh
Which parameters are borderline significant/not-significant; why
Which parameter is the most significant; least significant; why
2

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1. Regression is used to find the relationship between independent variables and a dependent variable. Then the relation can be used to make the future predictions of dependent values based on independent variables. The set of independent variables are also termed as predictors and dependent variable as response variable. E.g. if we want to find the relationship between the cost of house on the basis of its area, number of bedrooms, num of floor etc, the cost is the response variable while all other parameters are predictors. Regression can be used to find the weight/coefficient given to each predictor

which can be used to estimate the cost of the house. For example the relation can be:

cost = 10000*area + 5000*num_of_beds - 100 * floor_number.

It shows increase of one unit of area increases the cost by 10000 times. Similarly, each increase of floor number deceases the cost of house by a factor of 100. This is an example of simple linear regression.

Similarly, a combination of predictors can be used as a predictor, this type of regression is called the multiple regression. Regression using predictors with power more than one are called polynomial regression....