5. Interpret all slopes The data set shown in the DATA sheet were collected to s
ID: 3220497 • Letter: 5
Question
5. Interpret all slopes
The data set shown in the DATA sheet were collected to study the relationship between GPA, hours of spending watching TV, and the academic standing. 1. Recode the data for a multiple regression model 2. Interpret the significant F 3. Interpret the adjusted R square 4. Interpret the intercept5. Interpret all slopes
GPA Hours TV Year 3.29 2 Senior 2.65 24 Sophomore 1.94 27 Freshman 3.39 8 Junior 3.59 13 Senior 3.42 14 Junior 3.22 6 Junior 3.45 11 Sophomore 3.57 15 Senior 3.42 7 Junior 2.88 20 Freshman 3.38 13 Junior 3.04 20 Junior 3.08 20 Freshman 3.32 13 Junior 2.26 25 Freshman 3.13 19 Freshman 3.62 9 Senior 3.19 15 Sophomore 2.23 25 Freshman 3.44 13 Sophomore 3.32 4 Senior 3.07 18 Sophomore 3.27 14 Junior 3.47 15 Senior 2.4 24 Freshman 3.36 17 Sophomore 3.35 4 Senior 2.25 26 Sophomore 2.93 20 Freshman 2.79 22 Freshman 3.63 10 Junior 2.49 22 Freshman 3.29 2 Senior 3.4 3 Senior 3.44 12 Senior 3.51 16 Sophomore 3.12 20 Junior 2.9 20 Sophomore 2.43 24 FreshmanExplanation / Answer
1. Recode the data for a multiple regression model
Answer:
For the given multiple regression model, we have to predict the values for dependent variable GPA based on the two independent variables such as hours TV and year. We are given a ordinal scale for the variable year such as senior, sophomore, junior and freshman. So, we need to recode the data for this variable for the conduction of the multiple regressions. We will codes the values from 1 to 4 for the given four levels of academic year. We will use code ‘1’ for freshman, ‘2’ for junior, ‘3’ for sophomore and ‘4’ for senior.
2. Interpret the significant F
Answer:
For the given regression model, the ANOVA table for checking the significance of the given regression model is given as below:
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.790a
.624
.603
.28001
a. Predictors: (Constant), Year, Hours TV
ANOVA
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
4.692
2
2.346
29.919
.000a
Residual
2.823
36
.078
Total
7.514
38
a. Predictors: (Constant), Year, Hours TV
b. Dependent Variable: GPA
Coefficients
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
3.596
.234
15.378
.000
Hours TV
-.042
.008
-.689
-5.117
.000
Year
.056
.052
.144
1.073
.291
a. Dependent Variable: GPA
For this regression model, the test statistic value F is given as 29.919 with the p-value of 0.00. For this regression model, we get the p-value less than the level of significance or alpha value 0.05, so we reject the null hypothesis that the given regression model is not statistically significant. So, we conclude that there is sufficient evidence that the given regression model is statistically significant.
3. Interpret the adjusted R square
Answer:
The value of the adjusted R square or adjusted coefficient of determination is given as 0.603, this means about 60.3% of the minimum variation in the dependent variable GPA is explained by the independent variables year and TV hours.
4. Interpret the intercept
Answer:
For the given regression model, the value of the Y-intercept is given as 3.596. The p-value for t test for checking the significance of intercept is given as 0.00 which is less than alpha value 0.05. So, we reject the null hypothesis that the intercept for this regression model is not statistically significant. This means we conclude that the intercept for this regression model is statistically significant.
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.790a
.624
.603
.28001
a. Predictors: (Constant), Year, Hours TV
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