Estimate a simple regression model, Sales=β0+β1Advertising+ε,Sales=β0+β1Advertising+ε, as well as a multiple regression model, Sales=β0+β1Advertising+β2Unemployment+ε.Sales=β0+β1Advertising+β2Unemployment+ε.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Akiko Hamaguchi, the manager at a small sushi restaurant in Phoenix, Arizona, is concerned that the weak economic environment has hampered foot traffic in her area, thus causing a dramatic decline in sales. Her cousin in San Francisco, Hiroshi Sato, owns a similar restaurant, but he has seemed to prosper during these rough economic times. Hiroshi agrees that higher unemployment rates have likely forced some customers to dine out less frequently, but he maintains an aggressive marketing campaign to thwart this apparent trend. For instance, he advertises in local papers with valuable two-for-one coupons and promotes early-bird specials over the airwaves. Despite the fact that advertising increases overall costs, he believes that this campaign has positively affected sales at his restaurant. In order to support his claim, Hiroshi provides his restaurant’s monthly sales (in $1,000s) and advertising costs (in $), as well as the monthly unemployment rate (in %) from San Francisco County. A portion of the data is shown in the accompanying table.
| Month | Year | Sales | AdsCost | Unemp |
| Jan | 2008 | 27 | 550 | 4.6 |
| Feb | 2008 | 24.2 | 425 | 4.3 |
| Mar | 2008 | 25.6 | 450 | 4.6 |
| Apr | 2008 | 28.5 | 625 | 4.3 |
| May | 2008 | 30.8 | 650 | 4.8 |
| June | 2008 | 31.5 | 675 | 5.2 |
| July | 2008 | 34.9 | 700 | 5.6 |
| August | 2008 | 32.5 | 650 | 5.8 |
| Sept | 2008 | 30.4 | 550 | 5.5 |
| Oct | 2008 | 31 | 525 | 5.8 |
| Nov | 2008 | 28.5 | 500 | 6 |
| Dec | 2008 | 29 | 600 | 6.5 |
| Jan | 2009 | 26.2 | 575 | 8 |
| Feb | 2009 | 25.4 | 625 | 8.4 |
| Mar | 2009 | 27.8 | 650 | 9.1 |
| Apr | 2009 | 26.5 | 600 | 8.9 |
| May | 2009 | 27.4 | 550 | 9.1 |
In a report, use the sample information to
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Estimate a simple regression model, Sales=β0+β1Advertising+ε,Sales=β0+β1Advertising+ε, as well as a multiple regression model, Sales=β0+β1Advertising+β2Unemployment+ε.Sales=β0+β1Advertising+β2Unemployment+ε.
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Show that the multiple regression model is more appropriate for making predictions.
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Make predictions for sales with an unemployment rate of 6% and advertising costs of $400 and $600.
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