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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.

2) The Tenaga Elektik MN Company is studying the relationship between kilowatt-hours (thousands) used and the number of room in a private single-family residence. A random sample of 10 homes yielded the following.

Number of rooms | Kilowatt-Hours (thousands) | 12 9 14 6 10 8 10 10 5 7 | 9 7 10 5 8 6 8 10 4 7 |

a. Identify the independent and dependent variable.

b. Compute the coefficient of correlation and explain.

c. Compute the coefficient of determination and explain.

d. Test whether there is a positive correlation between both variables. Use α=0.05.

e. Determine the regression equation (used Least Square method)

f. Determine the value of kilowatt-hours used if number of rooms is 11.

g. Can you use the model in (f.) to predict the kilowatt-hours if number of rooms is 20? Explain your answer.

3) Mr Rama, president of Dan Din Dun Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr Rama gathered the following sample information. The X indicates the number of client contacts last month, and the Y shows the value of sales (RM thousands) last month...

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...relationships between the variables. The relationships can either be negative or positive. This is told by whether the graph increases or decreases. Benefits and Intrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.069642247 R Square 0.004850043 Adjusted R Square -0.00471871 Standard Error 0.893876875 Observations 106 ANOVA df SS MS F Significance F Regression 1 0.404991362 0.404991 0.50686 0.478094147 Residual 104 83.09765015 0.799016 Total 105 83.50264151 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.506191723 0.363736853 15.13784 4.8E-28 4.784887893 6.2274956 4.7848879 6.22749555 Benefits -0.05716561 0.080295211 -0.711943 0.47809 -0.21639402 0.1020628 -0.216394 0.10206281 Y=5.5062+-0.0572x Graph Benefits and Extrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.161906 R Square 0.026214 Adjusted R Square 0.01685 Standard Error 1.001305 Observations 106 ANOVA df SS MS F Significance F Regression 1 2.806919 2.806919 2.799606 0.097293 Residual 104 104.2717 1.002612 Total 105 107.0786 Coefficients Standard Error t Stat P-value Lower 95% Upper......

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