2. Types of graphs Scatter diagram: A graph of the value of one variable against the value of another variable Time-series graph: A graph that measures time on the x-axis and the variable or variables of interest on the y-axis. Cross-section graph: A graph that shows the values of a variable for different groups in the population at a point in time.

3. www.bea.gov 1991 Scatter diagram 1959 1999

4. Time-series graph

6. Unemployment rates in industrialized countries, May 2000 Source: The Economist Cross- section graph

8. Relationships among variables Variables X and Y have a positive or direct relationship if, ceteris paribus, they move in the same direction. Variables X and Y have a negative or inverse relationship if, ceteris paribus, they move in opposite directions. The relationship between X and Y is linear if it can be described by a straight line.

9. Distance traveled in 5 hours (miles) Speed (MPH) 4060 200 300 0

10. Recovery time (MINUTES) Distance sprinted (Yards) 200 20 30 0100400

11. Time partying (Hours) Time studying (Hours) 5 0 5

12. Advertising ($1,000’s per Mo.) Sales ($1,000’s per Mo.) 040 246 349 658 761 1173 1276 Linear graphs The Jewelry Mart

13. We want to describe the (causal) relationship between sales and advertising using a simple linear equation—because, as it turns out, the relationship is linear Let Y denote sales per month (in $1,000’s) Let X denote advertising per month (in $1,000’s) Thus we have: Y = f(X) Where Y is the dependent variable and X is the independent (explanatory variable)

14. Sales ($1,000’s per mo.) Advertising ($1,000’s per mo.) 0 40 76 49 46 231112 73 A E B F

15. Now we want to describe the relationship by a linear equation like this: Y = a + bX Where a is the intercept and b is the slope coefficient.

16. Y X 0 a > 0 a < 0 a = 0

18. a b > 0 b = 0 b < 0 0 Y X

19. Sales ($1,000’s per mo.) Advertising ($1,000’s per mo.) 0 40 76 49 46 231112 73 A E B F Now let’s compute the slope of this line Notice that a = $40

20. Moving from point A to B (or from point E to F), the vertical change is $3 and the horizontal change is $1. Thus our slope is equal to 3 Interpretation: A $1,000 increase in monthly advertising expenditures will result in a $3,000 increase in monthly jewelry sales(and vice-versa), other things being equal.

21. Thus we have: Y = 40 + 3X Suppose that the management of the Jewelry Mart have set a monthly sales target of $64,000. How much advertising is necessary to meet the target? Y = 40 + 3X Hence: 64 = 40 + 3X  24 = 3X  X = 8 The Jewelry Mart needs to spend $8,000 per month on advertising to achieve the sales target.