Part 1: The Atlantic Tire and Muffler Company introduced a new line of all-season tires in January of Year 1. This line proved very popular and there has been strong growth in sales. The table below shows the sales numbers (in 1000s of units) by three-month period in Years 1 and 2. Year 1 1 1 1 2 2 2 2 Period Jan-Mar Apr-Jun Jul-Sept Oct-Dec Jan-Mar Apr-Jun Jul-Sept Oct-Dec t 1 2 3 4 5 6 7 8 Sales 23 47 55 80 82 128 136 157 1. Using linear regression, what is the slope of the best fit line to the sales data? 2. Using linear regression, what is the intercept of the best fit line to the sales data? 3. If the best fit line is used to forecast the sales in Apr-Jun Year 3, what is the forecast sales figure (in 1000s of units)? 4. What is the forecast for sales in Apr-Jun Year 3 (in 1000s of units) if the forecast is adjusted with an additive adjustment? 5. What is the forecast for sales in Apr-Jun Year 3 (in 1000s of units) if the forecast is adjusted with a multiplicative adjustment?

Suppose sales for the past 6 months have been84, 81, 95, 87, 114, and 112 What is the 3-month moving average for the 4th period? (please round your answer to 1 decimal place)

Quarterly Glass Container Demand Year 1990 1991 1992 First Qtr. 17,446. 17,748. 17,595. Second Qtr. 17,785. 19,360. 18,338. Third Qtr. 18,971. Fourth Qtr. 19140. 17,802. 19,413. 18,315. 18,083. Question: Quarterly sales (in thousands of units) of a product over the last two years have been 26, 29, 30, 27, 28, 32, 33, and 30. Plot the data and forecast for the next period using Winter's Seasonal Model. Now, assume sales for the ninth quarter turned out to be 32. Update your parameter estimates and forecast sales for period 10.

A certain city's power company charges their residents for electricity usage on a daily basis. There is a basic charge of 11.57 cents. For each day the first 10 kWh cost 4.81 cents per kWh and any additional kWhs are 9.69 per kWh. (A kWh, or kilowatt-hour, is a unit of energy.) (a) Complete the following table using the information provided above. kWhkWh 0 5 10 15 20 cost (dollars)cost (dollars)           kWhkWh 25 30 35 40 cost (dollars)cost (dollars)         (b) We can define a piecewise function f(x)f(x) where xx is the kWh used in a day and f(x)f(x) is the cost, in dollars. This function would have the form   f(x)={g(x)h(x)ififx∈Ax∈Bf(x)={g(x)ifx∈Ah(x)ifx∈B What functions g(x)g(x) and h(x)h(x) make up the piecewise function f(x)f(x)? g(x)=g(x)= for A = h(x)=h(x)= for B = Hint: A and B are intervals. If an interval uses ±∞±∞ write inf or -inf . (c) Using the above function, what is the cost of 26 kWh? dollars. (d) For 3 dollars, what is the maximum kWh usage for one…

A certain company grants a six-month investment product that offers to pay its clients 8% the first month, 12% the second month, 11% the third month, 8% the fourth month, 14% the fifth month and 15% the sixth month. What would be the value of the average rate that the customer will receive? Write your answer to 2 decimal places.

8. Magazine Sales The following table shows the income, measured in thousands of dollars, from sales of a certain magazine at the start of the given year.

An entrepreneur who owns and operates two businesses (A and B) would like to analyze their profitability. They would like your help in the analysis. They give you the annual net profit (in thousands of $) for each business from 2008-2020. Table 1: Annual Net Profits for Businesses A and B Business Year Profit Business Year Profit 2008 -50 2008 -10 2009 57 2009 30 2010 71 2010 27 2011 64 2011 22 2012 60 2012 21 2013 50 2013 20 A 2014 41 2014 24 2015 59 2015 24 2016 71 2016 32 2017 71 2017 36 2018 74 2018 37 019 81 20 40 2020 97 2020 49 a. Suppose you want to graph the distribution of profits. Explain why using only one stem- plot might not be optimal for the analysis. b. Describe the correct stemplot to use. Generate this stemplot. Explain your steps. What can you say about the distribution from this stemplot? c. When are stemplots useful? And why is that? d. Suppose that instead of having 26 observations you have 200 observations. What graph should you generate? e. What other type of…