The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars.

Predictor Coefficient SE Coefficient t p-value
Constant 7.267 3.000 2.422 0.010
x1 0.237 0.220 1.077 0.000
x2 â1.162 0.554 â2.097 0.028
x3 â0.130 0.408 â0.319 0.114
x4 0.538 0.371 1.450 0.001
x5 â0.038 0.030 â1.267 0.112

Analysis of Variance
Source DF SS MS F p-value
Regression 5 2,385.91 477.2 9.06 0.000
Residual Error 42 2,212.82 52.69
Total 47 4,598.73

x1 is the number of architects employed by the company.
x2 is the number of engineers employed by the company.
x3 is the number of years involved with health care projects.
x4 is the number of states in which the firm operates.
x5 is the percent of the firmâs work that is health careârelated.

Required:
a. Write out the regression equation.
b. How large is the sample? How many independent variables are there?

Answer:

y = 0.237x1 - 1.162x2 - 0.130x3 * 0.538x4 - 0.038x5 + 7.267

5 independent variables

Sample size = 48

Step-by-step explanation:

The table shows the ouorit of a multiple regression

The regression equation from the table is given by :

Coefficient = 7.267 = intercept

Predictor variables are : x1, x2, x3, x4, x5

x1 = 0.237

x2 = 1.162

x3 = 0.130

x4 = 0.538

x5 = 0.038

General form of multiple regression equation :

y = m1x1 + m2x2... + c

x1, x2,.. Are independent variables

m1, m2 = slope values of

Hence, we have ;

y = 0.237x1 - 1.162x2 - 0.130x3 * 0.538x4 - 0.038x5 + 7.267

The sample size

The number of independent variables :

x1 is the number of architects employed by the company.

x2 is the number of engineers employed by the company.

x3 is the number of years involved with health care projects.

x4 is the number of states in which the firm operates.

x5 is the percent of the firmâs work that is health careârelated.

x1, x2, x3, x4, x5 = 5 independent variables

DF Regression = k - 1

5 = k - 1 ; k = 5 +1 = 6

N - k = 42

N - 6 = 42

N = 42 + 6 = 48

Samole size = 48

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