You have been provided with data for Sales and Advertising. Assume there are no

outliers in the data.?a. Estimate this model using regression analysis...

Sales = ?0 + ?1*advertising + ?2*advertising 2

State the hypothesis that tests if a non-linear relationship exists between Sales and Advertising. ?

Based on your regression analysis what is your conclusion? Give reason. ?

b. What is the marginal impact of advertising on sales if advertising is increased from $1500 to $1600? What is the marginal impact on sales if advertising is increased from $2400 to $2500? Please comment on any differences.

c. Is there a lead/lag relationship between Advertising and Sales? That is, estimate this model ...

Sales t = ?0 + ?1*advertising t + ?2*advertising t2 + ?3*advertising t-1 What is your conclusion? Give reason.

Year 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 Advertising $ 451.00 $ 529.00 $ 543.00 $ 525.00 $ 549.00 $ 525.00 $ 578.00 $ 609.00 $ 504.00 $ 752.00 $ 613.00 $ 862.00 $ 866.00 $ 1,016.00 $ 1,360.00 $ 1,482.00 $ 1,608.00 $ 1,800.00 $ 1,941.00 $ 1,229.00 $ 1,373.00 $ 1,611.00 $ 1,568.00 $ 983.00 $ 1,046.00 $ 1,453.00 $ 1,504.00 $ 807.00 $ 339.00 $ 562.00 $ 745.00 $ 749.00 $ 862.00 $ 1,034.00 $ 1,054.00 $ 1,164.00 $ 1,102.00 $ 1,145.00 $ 1,012.00 $ 836.00 $ 941.00 $ 981.00 $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ Sales 921.00 934.00 976.00 930.00 1,052.00 1,184.00 1,089.00 1,087.00 1,154.00 1,330.00 1,980.00 2,223.00 2,203.00 2,514.00 2,726.00 3,185.00 3,351.00 3,438.00 2,917.00 2,359.00 2,240.00 2,196.00 2,111.00 1,806.00 1,644.00 1,814.00 1,770.00 1,518.00 1,103.00 1,266.00 1,473.00 1,423.00 1,767.00 2,161.00 2,336.00 2,602.00 2,518.00 2,637.00 2,177.00 1,920.00 1,910.00 1,984.00 1993 1994 1995 1996 1997 1998 1999 2000 $ $ $ $ $ $ $ $ 974.00 766.00 920.00 964.00 811.00 789.00 802.00 770.00 $ $ $ $ $ $ $ $ 1,787.00 1,689.00 1,866.00 1,896.00 1,684.00 1,633.00 1,657.00 1,569.00