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# Performing a Complete Regression Analysis using Given Data

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An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model.
∑X = 40
∑X2 = 200
∑Y = 70
∑Y2 = 545
∑XY = 300

Find the estimated y intercept and slope and write the equation of the least squares regression line. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation and check the relation between coefficient of correlation and coefficient of determination. Finally, perform the test of significance of the slope coefficient.

https://brainmass.com/statistics/coefficient-of-determination/performing-complete-regression-analysis-data-587355

#### Solution Preview

SSx=Σ(x^2)-{(Σx)^2/n}=200-(40^2)/20=120

SSxy=Σxy-{ΣxΣy/n}=300-(40*70)/20=160

Slope=SSxy/SSx=160/120=1.33

Intecept=(Σy/n)-(Σx/n)β1=0.83

So equation of ...

#### Solution Summary

THe solution gives detailed steps on performing a complete regression analysis using given data: calculating slope, intercept, regression line, standard error, Mean Square Error, coefficient of determination and coefficient of correlation

\$2.19

## Statistics: Coefficient and Confidence interval - mean

See attached file for 3 problems: time for Speedy-Lub oil change, Google manager's salaries, Accu-Copiers' service times

2. The length of time to do a complete full service oil change at Speedy-Lube is normally distributed with a mean of 15.8 minutes and a standard deviation of 2.2 minutes
X P(X < x) P(X > x) Mean Std dev
11 .0146 .9854 15.8 2.2
15 .3581 .6419 15.8 2.2
21 .9910 .0090 15.8 2.2
24 .9999 .0001 15.8 2.2
p(lower) p(upper)

(A) Analyze the output above to determine what percentage of complete full service oil changes will fall between 15 and 21 minutes.
(B) What percentage of complete full service oil changes will take less than 11 minutes? If 1000 cars had a complete full service oil change, how many would you expect to be finished in less than 11 minutes?

3. A random sample a 16 Google mangers yield the following information on annual salaries. The sample mean is \$79,000, with a sample standard deviation of \$6,000. What is the mean salary of all Google managers? What is the 95% confidence interval for the population mean?

Confidence interval - mean

95% confidence level
79000 mean
6000 std. dev.
16 n
2.131 t (df = 15)
3197.174 half-width
82197.174 upper confidence limit
75802.826 lower confidence limit

4. Accu-Copiers, Inc. sells and services the Accu-500 copying machine. As part of its standard service contract, the company agrees to perform routine service on this copier. To obtain information about the time it takes to perform routine service, Accu-Copiers has collected data for 11 service calls. The service calls information revealed the following:
Refer to the MegaStat output below to answer questions A through G.

(A) Analyze the above output to determine the regression equation.

(B) What conclusions are possible using the meaning of b0 (intercept) and b1
(regression coefficient) in this problem? (That is, explain the meaning of the coefficients.)

(C) What conclusions are possible using the coefficient of determination (r-squared)?

(D) Calculate the coefficient of correlation. Interpret this value.

(E) Does this data provide significant evidence (a=0.05) that the time to perform routine services is associated with the number of copiers serviced? Find the p-value and interpret.

(F) Predict the average number of minutes required to service four copiers.

(G) What is the 95% confidence interval for the number of minutes required for four copiers requiring service? What conclusion is possible using this interval?

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