regression analysis project paper

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Sheet1

https://www.amacad.org/humanities-indicators/public-life/art-museum-attendance#31768
Year Age Level Percentage of Americans Who Visited an Art Museum in the Previous 12 Months Under 18 Above 35 SUMMARY OUTPUT
1982 Under 18 29.7 1 0
Between 18-35 24.6 0 0 Regression Statistics
Above 35 18.7 0 1 Multiple R 0.7117058936
1987 Under 18 29.9 1 0 R Square 0.506525279
Between 18-35 26.7 0 0 Adjusted R Square 0.4654023856
Above 35 23.6 0 1 Standard Error 2.3984176883
1992 Under 18 32.2 1 0 Observations 27
Between 18-35 29.1 0 0
Above 35 28.9 0 1 ANOVA
1997 Under 18 29.6 1 0 df SS MS F Significance F
Between 18-35 26.5 0 0 Regression 2 141.7088888889 70.8544444444 12.3173550526 0.000208535
Above 35 25.6 0 1 Residual 24 138.0577777778 5.7524074074
2002 Under 18 29.1 1 0 Total 26 279.7666666667
Between 18-35 24.7 0 0
Above 35 22.5 0 1 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
2007 Under 18 27.6 1 0 Intercept 25.1222222222 0.7994725628 31.4234951799 5.19272358118699E-21 23.4721919499 26.7722524946 23.4721919499 26.7722524946
Between 18-35 22.5 0 0 Under 18 3.5222222222 1.130624941 3.1152879213 0.0047113614 1.1887270328 5.8557174117 1.1887270328 5.8557174117
Above 35 20.3 0 1 Above 35 -2.0222222222 1.130624941 -1.7885880179 0.0863130529 -4.3557174117 0.3112729672 -4.3557174117 0.3112729672
2012 Under 18 26.1 1 0
Between 18-35 22.0 0 0
Above 35 21.7 0 1
2017 Under 18 26.7 1 0
Between 18-35 24.8 0 0
Above 35 23.5 0 1
2019 Under 18 26.9 1 0
Between 18-35 25.2 0 0
Above 35 23.1 0 1
Note:
Under 18 = Art museum visitors who are under 18 years old (visited outside school)
Between 18-35 = Art museum visitors who are between 18 to 35 years old
Above 35 = Art museum visitors who are above 35 years old

Sheet2

Copy values from the regression output table:
Coefficients SE
Intercept 25.1222222222 0.7994725628
Under 18 3.5222222222 1.130624941
Above 35 -2.0222222222 1.130624941
Question: Is there significant evidence that art museum attendance rate for American visitor who under 18 years old is higher than the age between 18-35 years old? Use α = 0.05.
H0 Ha
Step 1 Hypothesis β1 = 0 β1 > 0
Tested value 0
Step 2 Sample size 27
b (β estimate) 3.52222
SE 1.13062
t-value 3.1153
Step 3 DF 24
α 0.05
Type of test upper one tailed
Upper CV 1.7109 (from the CV calculator)
Lower CV n/a (from the CV calculator)
Decision rule Reject H0 in favor of Ha if the t-value > the upper CV.
Step 4 Decision Reject H0 in favor of Ha at α = 0.05.
Conclusion: There is significant evidence that art museum attendance rate for American visitor who under 18 years old is higher than the age between 18-35 years old (α = 0.05).

Sheet3

Copy values from the regression output table:
Coefficients SE
Intercept 25.1222222222 0.7994725628
Under 18 3.5222222222 1.130624941
Above 35 -2.0222222222 1.130624941
Question: Is there significant evidence that American visitors who are above 35 years old tend to have a lower art museum attendance rate compared to the American visitors who are between 18-35 years old? Use α = 0.05.
H0 Ha
Step 1 Hypothesis β2 = 0 β2 < 0
Tested value 0
Step 2 Sample size 27
b (β estimate) -2.02222
SE 1.13062
t-value -1.7886
Step 3 DF 24
α 0.05
Type of test lower one tailed
Upper CV n/a (from the CV calculator)
Lower CV -1.7109 (from the CV calculator)
Decision rule Reject H0 in favor of Ha if the t-value < the lower CV.
Step 4 Decision Reject H0 in favor of Ha at α = 0.01.
Conclusion: There is significant evidence that American visitors who are above 35 years old tend to have a lower art museum attendance rate compared to the American visitors who are between 18-35 years old (α = 0.05).

Sheet4

Copy values from the regression output table:
Coefficients SE LB of 95% CI UB of 95% CI
Intercept 25.1222222222 0.7994725628 23.4721919499 26.7722524946
Under 18 3.5222222222 1.130624941 1.1887270328 5.8557174117
Above 35 -2.0222222222 1.130624941 -4.3557174117 0.3112729672
Question: Show how to calculate a 95% confidence interval for the β1 coefficient. How do you interpret the interval estimate in the context of the problem here?
Output Table: LB of the CI 1.189
UB of the CI 5.856
Verifying with Our Own Calculation
Sample size 27
b (β estimate) 3.5222
SE 1.1306
DF 24
a 0.05
Upper CV 2.0639 (from the CV calculator)
Lower CV -2.0639 (from the CV calculator)
CI Calculation: MOE 2.3335
LB of the CI 1.189
UB of the CI 5.856
Interpretation: The 95% CI for β1 = [1.189, 5.856]. It is estimated that the art museums attendance rate under the age of 18 is generally higher than that of those between the ages of 18 and 24 by an average 1.189 to 5.856 percentage points.

Sheet5

From the Regression Output Table:
Statistic
R2 0.506525279
Question: What does the R2 value tell us? Interpret the R2 value in the context of the problem here.
Interpretation: The model's R2 value is around 0.5065. It means that age factor can account for about 50.65% of the variation in the data for art museum attendance rate by American visitors.

Sheet6

Copy values from the regression output table:
Coefficients SE
Intercept 25.1222222222 0.7994725628
Under 18 3.5222222222 1.130624941
Above 35 -2.0222222222 1.130624941
Question: Provide average estimates for Americans art museum attendance rate in the age group of under 18 years old, between 18-35 years old, and above 35 years old.
Coefficient Estimates from Excel's Output Table:
b0 b1 b2
25.12222 3.52222 -2.02222
Values for Predicting Variables: E(HSTART) = b0 + b1×SPRING + b2×SUMMER + b3×FALL
Age Group Under 18 Above 35 Estimates Formula used:
Under 18 1 0 28.644 =$B$15 + SUMPRODUCT($C$15:$E$15,C18:E18)
Between 18-35 0 0 25.122 =$B$15 + SUMPRODUCT($C$15:$E$15,C19:E19)
Above 35 0 1 23.100 =$B$15 + SUMPRODUCT($C$15:$E$15,C20:E20)
Conclusion: The average estimates of Americans art museum attendance rate are 28.6% for the age under 18 years old , 25.1% for the age between 18-35 years old, and 23.1% for the age above 35 years old.