## A sample of students was taken measuring the hours studied for a test

**2- ** A sample of students was taken measuring the hours studied for a test and the score on the test (out of a possible total of 350 points)

__ X____(# hours study)__ __Y (Score on test)__

5 155

7 210

8 150

10 192

11 245

13 260

15 270

18 275

20 290

a). Give the following:

i) sum of the x

ii) sum of the y

iii) sum of the x squared

iv) sum of the xy

v) sum of the y squared

b) Find b sub 0 and b sub 1 using the formulas in Excel that were used in the module. Round to 3 decimal places.

c) Find the equation of the regression line.

d) What is the value of the slope and interpret its meaning in the context of this problem

e) Predict the test score for 13 hours of study.

f) Calculate the coefficient of determination by writing the formula in Excel. Show your calculations.

g) What % of the variation in test scores is explained by the # hours of study?

h) What % is due to other factors?

i) Name 1 other factor that could affect a test score.

j) What is the calculated F in testing the null hyothesis: no significant relation between # hours of study and test scores. (You must use the Tool-Pak for this.)

k) What is the p-value?

l) Is there a significant relation between #hours of study and test scores? Please answer yes or no

**3-** The following data give the sales in millions of dollars for a company for the given years:

__Years__ __Sales__

2001 3.1

2002 3.6

2003 4.3

2004 4.9

2005 5.2

2006 6.1

2007 6.9

2008 7.2

a) Give the equation of the trend line for this time series. Round to 3 decimal places.

b) Interpret the intercept in the context of this problem. Move decimal appropriately in your answer.

c) Interpret the slope of sales in the context of this problem. Move decimal appropriately in your answer.

d) Forecast sales for the year 2012. Move decimal appropriately in your answer.

e) What % of the increase in sales is explained by the lineaer trend over the time series?

**4**. The data below represent Y, sales in thousands of dollars; X1, price in cents; X2, promotion in dollars.

**Sales****Price**** Promotion**

53 674 3250

59 628 3589

61 536 4266

63 521 4875

65 528 4912

71 506 5763

76 453 6173

83 399 6369

a) Give the equation of the regression line. Round to 3 decimal places.

b) Give the value of the slope for price

c) Interpret its meaning in the context of this problem. Move ethe decimal appropriately

d) Give the value of the slope for promotion.

e) Interpret its meaning in the context of this problem. Move the decimal appropriately.

f) Predict sales for price of $4.50 and $6000 spent on promotion. Move the decimal appropriately.

g) Give the calculated F for testing if the relationship is significant between sales & price and promition.

h) What is its p-value?

i) Is the relationship significant? Please answer yes or no.

j) Give the coefficient of determination.

k) Interpret its meaning in the context of this problem.

l) Give the coefficient of partial determination for price. Show your calculations.

m) Interpret its meaning in the context of this problem.

n) Give the coefficient of partial determination for promotion. Show your calculations.

o) Interpret its meaning in the context of this problem.

**5.** Your factory produces 5 styles of coats. There are 5 rectangular areas (length and width in ft. are given) for each style of coat. Workers are paid $25 per hour. From the data below, find **for each style****:**

1) the total wholesale $, 2) the total wages paid, 3) the total production cost, 4) the costs + wages as % of wholesale $. Remember wholesale $ is only for acceptable coats as we don’t sell rejects. Production costs are in dollars.

Style of coat: __length of area__ __width of area__ __#acceptable__ __#rejected__ __prod. cost$ each coat/sq. ft.__ __wholesale$/coat__ __# worker hrs/coat__

1 135 95 5786 452 .02 435 3.5

2 120 105 4468 354 .04 347 4.1

3 140 120 5637 259 .03 320 3.9

4 130 80 4903 395 .01 310 3.1

5 125 90 4039 349 .02 298 2.9