Question

Solve the problem.

21) The total home-game attendance for major-league baseball is the sum of all attendees for all stadiums during the entire season. The home attendance (in millions) for a number of years is shown in the table below.

21)

Year

Home Attendance (millions)

1978

40.6

1979

43.5

1980

43.0

1981

26.6

1982

44.6

1983

46.3

1984

48.7

1985

49.0

1986

50.5

1987

51.8

1988

53.2

a) Make a scatterplot showing the trend in home attendance. Describe what you see.

b) Determine the correlation, and comment on its significance.

c) Find the equation of the line of regression. Interpret the slope of the equation.

d) Use your model to predict the home attendance for 1998. How much confidence do you have in this prediction? Explain.

e) Use the internet or other resource to find reasons for any outliers you observe in the

scatterplot.

Answer 1

a.

From the scatter plot it is observed that "Year" and "Home attendance" are linearly related and for most of the cases we observe that as "Year" increases "Home attendance" also increases hence two variables are positively correlated.

b.

Pearson correlation of Year and Home Attendance (millions) = 0.688
P-Value = 0.019
Since p-value<0.05 hence there exists significant linear relation between two variables "Year" and "Home attendance".

c.

The regression equation is
Home Attendance (millions) = - 2976 + 1.52 Year
If we increase "year" by one unit then Home Attendance is increased by 1.52 millions.

d.

Predicted home attendance when Year=1998=-2976+1.52*1998= 60.96 millions

However we have not enough confidence about this estimate since we have no idea about the relationship between these two variables outside the range.

e. From scatter plot we observe that there is one outlier i.e. (1981,26.6).