7. a. Develop a linear trend equation for the following data on demand for white bread loaves at a bakery (use of Excel's Trendline, with display equation on chart option, is recommended), and use it to forecast demand on day 16. Day Loaves Day 1 200 6 2 214 7 3 211 8 228 9 235 10 4 5 Loaves 232 248 250 253 267 Day 11 12 13 14 15 Loaves 281 275 280 288 310 b. The variations around the linear trend line seem to have above- and below-the-line runs. Therefore, use trend-adjusted exponential smoothing with a = 0.3 and ß = 0.2 to model the bread demand. Use the first four days to estimate the initial smoothed series (use the average of the first four days) and smoothed trend (use the increase from day 1 to day 4 divided by 3). Start forecasting day 5. What is the forecast for day 16?

3. The police department is assessing its staffing requirements. The department expects that the number of serious crimes committed, C, on average each week is proportional to the number of officers, P, on special street patrol. Data for the past year has been collected and some of it is shown below: P 4 7 9 11 15 17 с 14 11 10 9 7 5 a) Neatly sketch a scatter plot of the data on graph provided below. Which variable is the independent variable that should be plotted on the horizontal axis? Notice that the data seem to fall in a linear pattern. Draw the best-fit line through the data. Label your axes, indicate the scale, and title your graph. Why has only the first quadrant been provided for the graph? b) Look at your best-fit line and identify two good coordinate points that sit right on this best-fit line:

A company has the following monthly sales for the past year.  Plot the data points on a line graph and describe the results. Month Sales 1 145 2 146 3 145 4 150 5 148 6 150 7 156 8 160 9 158 10 153 11 152 12 154

For the data set, perform exponential smoothing with alpha = 0.1 to determine the forecast for week 20.   week Sales (1000s of gallons) 1 17 2 21 3 19 4 23 5 18 6 16 7 20 8 18 9 22 10 20 11 15 12 22 13 31 14 34 15 31 16 33 17 28 18 32 19 30

The following time series shows the sales of supermarket chain over the last six months.  Month Sales ($ 000) August 2021 250 Sep 2021 280 Oct 2021 295 Nov 2021 320 Dec 2021 380 Jan 2022 360   Develop a linear trend equation that can be used to forecast sales in Feb 2022. Forecast the sales in Feb 2021 using a three-period weighted moving average designed with the following weights: Nov 2021 weight 0.6, Dec 2021 weight 0.3 and Jan 2022 weight 0.1. Which method (A or B) is the best? Explain why.

1.     A researcher is interested in knowing if there is a relationship between the years presented in the table below and the average number of people in a family receiving welfare benefits. Year Average Family Size 1969 4.0 1973 3.6 1975 3.2 1979 3.0 1983 3.0 1988 3.0 1991 2.9 a. What are your conclusions and observations about the relationship between the two variables b.What is the value of the intercept a? c. What is the value of the slope b? d. Write the linear regression equation

The following table shows the values of the age and the job satisfaction of ice cream shop employees Employee Age    Job Satisfaction16    918    920    722    824    426    528    626    524    722    8 d.  Sketch a scatterplot of this data by hand (do NOT use/submit any plots created by a program).e. Does there appear to be a linear relationship between the two variables? f.  Calculate the slope for this data.

The below data represent the advertising expenditure and sales of Little Liu Ltd from year 2008 to 2017.   Table: Advertising Expenditure vs. Sales from 2008 to 2017   Year Advert. Expenditure Sales   (x, £000) (y, £000) 2008 8 30 2009 12 40 2010 11 29 2011 5 29 2012 14 43 2013 3 17 2014 6 20 2015 8 30 2016 4 22 2017 9 40 Total 80 300   Figure: Scatter Diagram of Advertising Expenditure and Sales with Trend line ( See picture)   What is the statistical relationship shown in the Figure and list out 3 characteristics of this relationship?   2. Work out the values of parameters of the relationship shown in the Figure (i.e. work out the equation of the relationship).   3.Explain the relationship and make recommendations to Little Liu Ltd based on the information given.