## Assignment 4 – Business Faculty – Summer Semester

## Professor: Dr. Rosa Padilla de Casamayor

Follow the procedures covered in this chapter to generate appropriate to answer the following questions:

**Short answers**

1. The slope (*B1) *represents:
a. Predict value of y when x=0
b. Predict value of Y

c. Change in Y per unit change in X

2. The Y intercept (*B0) *represents the:
a. Change in Y per unit change in X
b. Predict value of y when x=0
c. Variation around the regression line

3. The coefficient of determination (r2_{) tells you:}

a. The proportion of total variation that is explained b. Whether the slope has any significance

c. Whether the regression sum of squares is greater than the total sum of squares

4. In performing a regression analysis involving two numerical variables, you assume: a. The variance of X and Y are equal

b. That X and Y are independent c. All of the above

5. The residuals represent:

a. The difference between the actual Y values and the mean of Y b. The square root of the slope

c. The difference between the actual Y values and the predicted Y values

6. If the coefficient of correlation (r) = -1.00, then:

a. All the data points must fall exactly on a straight line with a inverse or negative slope. b. All the data points must fall exactly on a straight line with a positive slope

c. All the data points must fall exactly on a horizontal straight line with a zero slope.

7. Assuming a straight line (linear) relationship between X and Y, if the coefficient of correlation (r) = -0.30: a. There is no correlation

b. Variable X is larger than variable Y c. The slope is negative

8. In a simple linear regression model, the coefficient of correlation and the slope: a. May have opposite signs

b. Must have the same sign c. Are equal

9. What is the role of F test in multiple regression?

10. Haverty’s Forniture is a family business that has been selling to retail customers in the Chicago area for many years. The company advertises extensively on radio, TV, and the internet, emphasizing low prices and easy credit terms. The owner would like to review the relationship between sales and the amount spent on advertising. Below is information on sales and advertising expense for the last four months.

Month Advertising Expense_{($ millions)} _{Revenue}Sales

July 2 7

August 1 3

September 3 8

*Note: in real life never use a small sample, here there is only one mathematical example for easy to calculate*

a. The owner wants to forecast sales on the basis of advertising expense. Which variable is the dependent variable? Which variable is the independent variable?

b. Draw and interpret a scatter diagram

c. Compute and interpret the coefficient of correlation

d. Compute and interpret the coefficient of determination within the context of this problem e. Compute the regression equation

f. Estimate sales for the month of November if invested in advertising 4.5 millions $

*Answer: r =.965*, Sig. = .035, r2 _{=93.1%, }*

_{, }11. The table below presents information on three variables for a small sample of 25 observations by year of these variables. These data will be used to develop a linear model that predicts annual profit margin as a function of revenue per deposit dollar and number of offices. The SPSS software report is given below, you verify and interpret all results:

Savings and loan Association Operating Data

Year Revenue perDollar Number ofOffices Profit Margin Year Revenue perDollar Number ofOffices Profit Margin

1 3.92 7298 0.75 14 3.78 6672 0.84

2 3.61 6855 0.71 15 3.82 6890 0.79

3 3.32 6636 0.66 16 3.97 7115 0.7

4 3.07 6506 0.61 17 4.07 7327 0.68

5 3.06 6450 0.7 18 4.25 7546 0.72

6 3.11 6402 0.72 19 4.41 7931 0.55

7 3.21 6368 0.77 20 4.49 8097 0.63

8 3.26 6340 0.74 21 4.7 8468 0.56

9 3.42 6349 0.9 22 4.58 8717 0.41

10 3.42 6352 0.82 23 4.69 8991 0.51

11 3.45 6361 0.75 24 4.71 9179 0.47

12 3.58 6369 0.77 25 4.78 9318 0.32

13 3.66 6546 0.78

**Correlations **

Margin Profit Revenue Number of Offices

**a.** Interpret the coefficient of correlation for each
pair:

Profit

Margin Pearson Correlation 1 -.704

** _{-.868}**

Sig. (2-tailed) .000 .000

N 25 25 25

Revenue Pearson Correlation _{-.704}** _{1 } _{.941}**

Sig. (2-tailed) .000 .000

N _{25 } _{25 } _{25 }

Number

of Offices Pearson Correlation -.868

** _{.941}** _{1 } _{ }

Sig. (2-tailed) _{.000 } _{.000 } _{ }

N 25 25 25

**b.** Interpret multiple correlation coefficients(R), and the coefficient of multiple determinations (R2_{). How much of the variance in}

Profit Margin is explained by the two independent variables?

**Model Summaryb**

Model R R Square Adjusted R Square Durbin-Watson

1 .930a _{.865} _{.853} _{1.948}

Multiple correlation coefficients(R) __________________________________________________________________________________
Multiple determinations coefficient (R2_{): ____________________________________________________________________________}

____________________________________________________________________________________________________________

Make assumption for aautocorrelated by Durbin Watson:________________________________________________________________ _____________________________________________________________________________________________________________

**ANOVAa** _{c}_{. Interpret ANOVA table: }

Model Sum of Squares df Mean Square F Sig.

1 Regression .402 2 .201 70.661 .000b _{ }

Residual .063 22 .003

Total .464 24

a. Dependent Variable: Profit Margin _{ }

b. Predictors: (Constant), Number of Offices, Revenue

**d.** Find the multiple regression equation with Revenue (x1) and Number of Offices (x2):

_____________________________________________________________________________________________

**Coefficientsa**

Model

Unstandardized

Coefficients Standardized Coefficients

t Sig.

B Std. Error Beta

1 (Constant) 1.564 .079 19.705 .000

Revenue .237 .056 .987 4.269 .000

Number of Offices .000 .000 -1.797 -7.772 .000

a. Dependent Variable: Profit Margin

**e.** What will be Profit Margin would be expected for Revenue of 4.8, and Number of offices of 9500?

_____________________________________________________________________________________________

**f.** Interpret assumptions: Errors has a Normal Distribution by graph and test of normality

Interpret:____________________ Interpret:________________________________________

**Tests of Normality**

Kolmogorov-Smirnova _{Shapiro-Wilk}

Statistic df Sig. Statistic df Sig.

Hypotheses testing to determine the normality

Ho: _____________________________________________________________________________ Ha:______________________________________________________________________________ Sig:_____________

Making Decision and interpret the result: _________________________________________________________________

12. The table below presents information on three variables for a small sample of eight nations. We will take abortion rate as the dependent variable and examine is relationship with two variables: one measures women’s status and power and the other measures religiosity.

Nation Abortion Rate (Y) Women's Status (x1) Religiosity (x2)

Canada 165 0.5 74

Chile 100 0.45 93

Denmark 400 0.8 48

Germany 208 0.54 67

Italy 389 0.7 70

Japan 379 0.52 55

UK 207 0.58 67

US 428 0.84 35

The SPSS software report is given below, you verify and interpret all output:

**a. Interpret the coefficient of correlation for at ;east one pair:_________________________________**

Scatter Plot:

**b.***Interpret:___________________________* Interpret:___________________________

**Model Summaryb**

1 _{.875}a _{.765} _{.671} _{73.19844} _{1.569}

*Predictors: (Constant), Religiosity (x2), Women's Status (x1)*

*Dependent Variable: Abortion Rate (Y)*

* c.* Interpret multiple correlation coefficients (R), and the coefficient of multiple determinations (R2

_{). (How much of the variance in abortion rate}

is explained by the two independent variables?).

* d.* Make assumption for autocorrelated by Durbin Watson:__________________________________

**ANOVAa**

Model

Sum of Squares df Mean Square F Sig.

1 Regression 87171.942 2 43585.971 8.135 .027b

Residual 26790.058 5 5358.012

Total 113962.000 7

*a. Dependent Variable: Abortion Rate (Y)*

*b. Predictors: (Constant), Religiosity (x2), Women's Status (x1)*

* e.* Interpret ANOVA table:_______________________________________________________

**Coefficientsa**

Model Unstandardized

Coefficients StandardizedCoefficients

t Sig.

B Std. Error Beta

1

(Constant) 310.885 345.19 0.901 0.409

Women's Status (x1) 348.413 317.472 0.398 1.097 0.322

Religiosity (x2) -3.789 2.624 -0.523 -1.444 0.208

*a. Dependent Variable: Abortion Rate (Y)*

* f.* Find the multiple regression equation with Women's Status (x1) and religiosity (x2).

* g.* What will be abortion rate would be expected for Women's Status 0.90, and religiosity of 90?

13. A market study for self-service retailer "Nakomatt" analyzes the annual amount that spent on food families of four or more members. It is thought that three independent variables are related to the cost of food. These variables are: total household income, family size and whether the family has children in college.

Family Expenditureon food Household income($ 1000) Familysize in collegeChildren

1 3900 37.6 4 0

2 5300 51.5 5 1

3 4300 41.6 4 0

4 4900 46.8 5 0

5 6400 53.8 6 1

6 7300 62.6 7 1

7 4900 54.3 5 0

8 5300 52.7 4 0

9 6100 60.8 5 1

10 6400 63.5 6 1

11 7400 64.2 8 1

**Interpret each table from outcome of SPSS**

Model Summaryb

Model R R Square Adjusted R Square Std. Error of the Estimate Durbin-Watson

1 .969a _{0.939} _{0.916} _{320.393} _{2.559}

*Predictors: (Constant), Children in college, Household income ($ 1000), Family size*
*Dependent Variable: Expenditure on food*

a. Interpret multiple correlation coefficients (R), and the coefficient of multiple determinations (R2_{). How much of the variance in Expenditure}

on food is explained by the three independent variables?

b. Make assumption for autocorrelated by Durbin Watson:____________________________________
**Coefficientsa**

Model Unstandardized Coefficients

Standardized

Coefficients t Sig.

B Std. Error Beta

(Constant) 35.405 767.913 .046 .964

Household income ($ 1000) 63.753 18.391 .493 3.467 .008

Family size 386.805 131.609 .432 2.939 .019

Children in college 275.684 275.936 .131 .999 .347

*Dependent Variable: Expenditure on food*

c. Find the multiple regression equation with Household income (x1) and family size(x2) and children in college (x3).