STATISTICS FOR ENGINEERS (EQT 373)
TUTORIAL CHAPTER 3 – INTRODUCTORY LINEAR REGRESSION
1) Given 5 observations for two variables, x and y.
| 3 | 12 | 6 | 20 | 14 |
| 55 | 40 | 55 | 10 | 15 |
a. Develop a scatter diagram for these data.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Develop the estimated regression equation by computing the values and.
d. Use the estimated regression equation to predict the value of y when x=10.
e. Compute the coefficient of determination. Comment on the goodness of fit.
f. Compute the sample correlation coefficient (r) and explain the result.
Number of Contacts, X | Sales (RM thousands), Y |
14 12 20 16 46 23 48 50 55 50 | 24 14 28 30 80 30 90 85 120 110 |
a. Compute the coefficient of correlation and explain.
b. Compute the coefficient of determination and explain.
c. Test whether there is a positive correlation between both variables. Use α=0.05.
d. Determine the regression equation.
e. Determine the value of sales if number of contacts is 25.
4) The commercial division of a real estate firm is conducting a regression analysis of the relationship between X, annual gross rents (in thousands of dollars) and Y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained.
FIGURE 1: MINITAB OUTPUT
The regression equation isY = 20.0 + 7.21 XPredictor Coef SE Coef TConstant 20.000 3.2213 6.21X 7.210 1.3626 5.29Analysis of VarianceSOURCE DF SS MSRegression 1 41587.3 41587.3Residual Error 7 10396.8 1485.26Total 8 51984.1 |
a. How many apartment buildings were in the sample?
b. Write the estimated regression equation.
c. Use F-statistic to test the significance of the relationship at a 0.05 level of significance.
d. Estimate the selling price of an apartment building with gross annual rents of $50,000.
5) Fill in the blanks.
i. For the multiple regression equation: , if increased by 10 units with and remain unchanged, the estimated value of Y would __________________by______________
ii. The differences between the true and fitted values for the points in sample are called as ____________________
6) The estimated regression equation for a model involving two independent variables and
10 observations follows:
i. Interpret and in this estimated regression equation
ii. Estimate Y when =180 and =310
7) A shoe store developed the following estimated regression equation relating sales to inventory
investment and advertising expenditure:
i. Estimate sales resulting from a $15000 investment in inventory and an advertising budget of $10000
ii. Interpret and in this estimated regression equation
8) The following estimated regression equation based on 10 observations was presented.
Here SST=6724.125, SSR= 6216.375, and
i. Compute and interpret its value
ii. Compute MSR and MSE
iii. Compute F and perform the appropriate F test. Use
iv. Is significant? Use
9) The owner of Showtime Movie Theaters,Inc., would like to estimate weekly gross
revenue as a function of television advertising...