Statistics SA is concerned about the number of professors in statistics. They modelled available data with the following regression function. Ŷ = bo + b₁X₁ + b₂X₂ + b3X3 where X₁ : X₂: X3: Ỹ: TIMES - Number of times as international congress speaker ART - Number of articles published YEARS Years after PhD to attain professorship MONEY - Money s received for research (R1000.00) An extract from the data set n = 40 Y₁ 145 120 125 105 X₁ 7 7 4 7 X₂ 5 70 60 85 X3 10 8 12 10 The regression model from SAS: Ỹ = 1 + 2X₁ + 5X₂ -0.1X3 1.1. Interpret the estimated regression function by interpreting the regression coefficients. 1.2. The analyst of Stats SA is not sure that if years to professorship contributes to the variation of the mean money value. How can he determine whether or not this is so? Show this if a variance- covariance matrix was obtained and found that s{b3} = 0.2. Use a = 0.05. 1.3. If it was found that B3 = 0, can one just then use the following regression? Ỹ = 1 + 2X₁ + 5X₂ -0.1X3
Statistics SA is concerned about the number of professors in statistics. They modelled available data with the following regression function. Ŷ = bo + b₁X₁ + b₂X₂ + b3X3 where X₁ : X₂: X3: Ỹ: TIMES - Number of times as international congress speaker ART - Number of articles published YEARS Years after PhD to attain professorship MONEY - Money s received for research (R1000.00) An extract from the data set n = 40 Y₁ 145 120 125 105 X₁ 7 7 4 7 X₂ 5 70 60 85 X3 10 8 12 10 The regression model from SAS: Ỹ = 1 + 2X₁ + 5X₂ -0.1X3 1.1. Interpret the estimated regression function by interpreting the regression coefficients. 1.2. The analyst of Stats SA is not sure that if years to professorship contributes to the variation of the mean money value. How can he determine whether or not this is so? Show this if a variance- covariance matrix was obtained and found that s{b3} = 0.2. Use a = 0.05. 1.3. If it was found that B3 = 0, can one just then use the following regression? Ỹ = 1 + 2X₁ + 5X₂ -0.1X3
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Transcribed Image Text:Statistics SA is concerned about the number of professors in statistics. They modelled available data
with the following regression function.
Ŷ = bo + b₁X₁ + b₂X₂ + b3X3
where
X₁ :
X₂:
X3:
Ŷ:
TIMES - Number of times as international congress speaker
ART - Number of articles published
YEARS - Years after PhD to attain professorship
MONEY - Money s received for research (R1000.00)
An extract from the data set n = 40
Y₁
145
120
125
105
X₁
7
7
4
7
X₂
5
70
60
85
X3
10
8
12
10
The regression model from SAS: Y = 1 + 2X₁ + 5X₂ - 0.1X3
1.1. Interpret the estimated regression function by interpreting the regression coefficients.
1.2. The analyst of Stats SA is not sure that if years to professorship contributes to the variation of the
mean money value. How can he determine whether or not this is so? Show this if a variance-
covariance matrix was obtained and found that s{b3} = 0.2. Use a = 0.05.
1.3. If it was found that B3 = 0, can one just then use the following regression?
Ỹ = 1 + 2X₁ + 5X₂ -0.1X3
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