M1 solns and REMARKS

# Coefficients standard error t stat p value constant

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Coefficients Standard Error t Stat P-value Constant XXXX 43.4074727 -15.0385889 5.9306E-21 Contacts 35.0008935 1.39830769 25.0308955 2.1802E-31 Correlation 0.92 36. Find the number that is missing in the output above (denoted by “XXX”.) Give it the proper label and include the units. a = ybar – b(xbar) xbar = 10 (given) ybar = 652 (given) b = slope = 35 (output) Solve to get a = 652 – 35(10) = 302 UNITS SOLD, or 302 SALES 7

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37. Suppose each unit sold results in a profit of \$100. How much profit are you expected to earn per contact ? Slope = 35 sales per contact Each sale results in \$100 profit Total profit per contact = 100(35) = \$3,500 Note that you are looking for the change in profit per ONE UNIT INCREASE in contacts. This is the slope. One common answer was to take y bar / x bar = 652 / 10 = 65.2 and multiply by \$100 to get \$6,520. This is incorrect because y bar/ x bar is not the formula for slope. The slope has to include a measure of how contacts and sales are related. Also, slope is how many more sales you make per ONE contact, not per the AVERAGE NUMBER of contacts. The slope in this problem is 35 = r Sy / Sx and is shown on the output. It is true that x bar, y bar is a point on the line, but it represents the average number of sales when the number of contacts EQUALS one. (Not when the average number of sales is one.) Partial credit was given as deemed appropriate. This question was very similar to what was on the HW. 38. The output below gives summary statistics for a dataset of 100 people. The variable “Years” measures years of education and “Salary” measures the person’s annual salary. Suppose you want to predict someone’s salary given the number of years of education they have. What is the slope of the regression line? Include units. Variable Mean StDev Salary 58293.51 22106.96 Years 9.264 2.792 Pearson Correlation: 0.805 X = years, Y = salary Sx = 2.792, Sy = 22106.96 (output) Correlation is 0.805 (output) Slope = r(Sy/Sx) = 0.805(22106.96/2.792) = 6373.96 \$ PER YEAR OF EDUCATION 39. Trying to make predictions for Y using values of X outside the range of where data is collected is called EXTRAPOLATION . (ONE WORD statistical answer only.) Note: In order to be effective at critiquing others’ statistics, it is important to be able to use precise statistical terminology when identifying and describing problems you find regarding samples and analyses. This is a term we used quite often in the class, in Recitation, and on HW. Variations of this term (subject to spelling errors) could not be accepted. 8
40. Match the histograms to their statistics by filling in the last row of the table below. Data Set A Data Set B Data Set C Data Set D Mean 5.5 1 6 5.5 Standard Dev 3.03 0 1.05 4.74 Corresponding Histogram 1 4 2 3 9

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