Assume you have collected the data below from a small sample of gas stations in
ID: 3272970 • Letter: A
Question
Assume you have collected the data below from a small sample of gas stations in five neighborhoods, along with their populations. Observations 1 2 3 4 5 Gas Prices $2.40 $2.60 $3.00 $3.00 $3.00 Population (in 00’s) 24 36 30 30 35 For the “gas price” variable, compute the following: a) Mean: b) Median: c) Mode: d) Variance: e) Std. Deviation: f) Compute the co-efficient of correlation, r, for “gas prices” and “population”
Given the information below (adapted from the salary data in the previous questions):
Model (regression) sum of squares = 985,000 N (sample size) = 1100
Error (residual) sum of squares = 6,265,000 k (predictors) = 2
a) Calculate the value of R-squared for this model (to two decimal places).
b) What are the degrees of freedom for the F statistic associated with the above.
Numerator df: Denominator df:
c) What is the average leverage of all cases in this model?
Fill in the highlighted blanks in the table below (which contains information different from above; sample size is still 1100):
ANOVA(b)
Sum of Squares
Df
Mean Square
F
Sig.
(SSM)
Regression
13,704
B[ii]
E[v]
G[vii]
.000(a)
(SSR)
Residual
519,890
C[iii]
(SST)
Total
A[i]
D[iv]
a Predictors: (Constant), Gender
b Dependent Variable: Starting Salary
A[i]:
B[ii]:
C[iii]:
D[iv]:
E[v]:
F[vi]:
G[vii]:
Sum of Squares
Df
Mean Square
F
Sig.
(SSM)
Regression
13,704
B[ii]
E[v]
G[vii]
.000(a)
(SSR)
Residual
519,890
C[iii]
F[vi](SST)
Total
A[i]
D[iv]
Explanation / Answer
From the given data, The ANOVA table is
a) R-Squared = 13704 / (13704+519890) = 0.02568
b) df of numerator = 2, denominator df = 1097
c)
a) Predictors: 2
b) A[i] = 13704+519890= 533,594
B[ii] = 2
C[iii] = 1100 - 3 =1097
d[iv] = 1099
E[V] = 13704 / 2 = 6852
F[vi] = 519,890 / 1097 = 8
G[vii] = 6852 / 8 = 856.5
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