Why do we need time n when we calculate SSTR? In other words, why n times (mean of a factor level - mean of total)^2 Could you give me some intuitive explanation or proof?
Here are my lecture notes.
Homework Answers
We start understanding this
problem from starting but you can see from page 2 also... 
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Why do we need time n when we calculate SSTR? In other words,
why n times...
Suppose that independent samples of sizes n1, n2, . . . , nk are taken from each of k normally di...
Suppose that independent samples of sizes n1, n2, . . . , nk are taken from each of k normally distributed populations with means μ1,μ2, . . . , μk and common variances, all equal to σ 2. Let Yi j denote the j th observation from population i, for j = 1, 2, . . . , ni and i = 1, 2, . . . , k, and let n = n1 + n2 + ··· + nk...
Problem 4: Complete the ANOVA table based on the following data: Replications Standard Deviation ...
Problem 4: Complete the ANOVA table based on the following data: Replications Standard Deviation Factor A Level 1 Level 2 Mean 15 ANOVA Table Degree Freedom of Sum of square Mean sum of F-valuc Source error square error Treatment Error Total NA NA NA Recall that for single-factor ANOVA, we have the following -SSTreatments+SSp where ss,-Σ Σ(y)-T)-total sum of squares n Σ(vi-r-treatment sum of squares i- SSE _ Σ Σ(w-5)2-error sum of squares Given a dataset like the following: Treatment...
Could you please explain the step 1 and step 2 for me? I know the notes...
Could you please explain the step 1 and step 2 for me? I know
the notes want to show the formula for E(SSTR), but I don't know
what are these two steps doing.
1.2 Expectations of sums of squares Expectation of the sums of squares be derived from the following fact about sample variance. If X1, . . . , Xn are iid, with mean μ and variance σ2, then The sample variance is an unbiased estimator of the variance...
Given are five observations for two variables, and y 3 6 14 16 19 yi 52 57 42 17 10 Use the estimated regression equation is ý 67.97 - 2.79z a. Compute the mean square error using equation SSE MS2 (t...
Given are five observations for two variables, and y 3 6 14 16 19 yi 52 57 42 17 10 Use the estimated regression equation is ý 67.97 - 2.79z a. Compute the mean square error using equation SSE MS2 (to 2 decimals) b. Compute the standard error of the estimate using equation. SSE n -2 (to 2 decimals) c. Compute the estimated standard deviation of bi using equation (to 4 decimals) d. Use the t-test to test the following...
The following ANOVA model is for a multiple regression model with two independent variables: Degrees of Sum of Mean Source Freedom Squares ...
The following ANOVA model is for a multiple regression model
with two independent variables:
Degrees
of
Sum
of
Mean
Source
Freedom
Squares
Squares
F
Regression
2
60
Error
18
120
Total
20
180
Determine the Regression Mean Square (MSR):
Determine the Mean Square Error (MSE):
Compute the overall Fstat test statistic.
Is the Fstat significant at the 0.05 level?
A linear regression was run on auto sales relative to consumer
income. The Regression Sum of Squares (SSR) was 360 and...
Lab Activity 6: Multiple Regression We are looking at the research question: Will positive affectivity (PA)...
Lab Activity 6: Multiple Regression We are looking at the research question: Will positive affectivity (PA) and social support (ASOCS) predict academic burnout (ABO) levels? Previous research has shown that people who have more positive affect tend to experience burnout less. Research has also shown that social support can help prevent burnout. Previous research has not found any relationship between positive affectivity and social support. | Descriptive Statistics Mean Std. Deviation N 3.3154 .92736 227 ABO PA 3.356 .6729 227...
Gain (V/V) R Setting Totals Averages Sample 1 Sample 2 Sample 3 4 ап 7.8 8.1...
Gain (V/V) R Setting Totals Averages Sample 1 Sample 2 Sample 3 4 ап 7.8 8.1 7.9 3 5.2 6.0 4.3 = 359.3 i=1 j=1 2 4.4 6.9 3.8 1 2.0 1.7 0.8 This is actual data from one of Joe Tritschler's audio engineering experiments. Use Analysis of Variance (ANOVA) to test the null hypothesis that the treatment means are equal at the a = 0.05 level of significance. Fill in the ANOVA table. Source of Variation Sum of Squares...
Gain (V/V) R Setting Totals Averages Sample 1 Sample 2 Sample 3 4 ап 7.8 8.1...
Gain (V/V) R Setting Totals Averages Sample 1 Sample 2 Sample 3 4 ап 7.8 8.1 7.9 3 5.2 6.0 4.3 = 359.3 i=1 j=1 2 4.4 6.9 3.8 1 2.0 1.7 0.8 This is actual data from one of Joe Tritschler's audio engineering experiments. Use Analysis of Variance (ANOVA) to test the null hypothesis that the treatment means are equal at the a = 0.05 level of significance. Fill in the ANOVA table. Source of Variation Sum of Squares...
Problem 4: Complete the ANOVA table based on the following data: Replications Standard Deviation Factor A Level 1 Level 2 Mean 15 ANOVA Table Degree Freedom of Sum of square Mean sum of F-valuc Source error square error Treatment Error Total NA NA NA Recall that for single-factor ANOVA, we have the following -SSTreatments+SSp where ss,-Σ Σ(y)-T)-total sum of squares n Σ(vi-r-treatment sum of squares i- SSE _ Σ Σ(w-5)2-error sum of squares Given a dataset like the following: Treatment...
Could you please explain the step 1 and step 2 for me? I know
the notes want to show the formula for E(SSTR), but I don't know
what are these two steps doing.
1.2 Expectations of sums of squares Expectation of the sums of squares be derived from the following fact about sample variance. If X1, . . . , Xn are iid, with mean μ and variance σ2, then The sample variance is an unbiased estimator of the variance...
Given are five observations for two variables, and y 3 6 14 16 19 yi 52 57 42 17 10 Use the estimated regression equation is ý 67.97 - 2.79z a. Compute the mean square error using equation SSE MS2 (to 2 decimals) b. Compute the standard error of the estimate using equation. SSE n -2 (to 2 decimals) c. Compute the estimated standard deviation of bi using equation (to 4 decimals) d. Use the t-test to test the following...
The following ANOVA model is for a multiple regression model
with two independent variables:
Degrees
of
Sum
of
Mean
Source
Freedom
Squares
Squares
F
Regression
2
60
Error
18
120
Total
20
180
Determine the Regression Mean Square (MSR):
Determine the Mean Square Error (MSE):
Compute the overall Fstat test statistic.
Is the Fstat significant at the 0.05 level?
A linear regression was run on auto sales relative to consumer
income. The Regression Sum of Squares (SSR) was 360 and...
Lab Activity 6: Multiple Regression We are looking at the research question: Will positive affectivity (PA) and social support (ASOCS) predict academic burnout (ABO) levels? Previous research has shown that people who have more positive affect tend to experience burnout less. Research has also shown that social support can help prevent burnout. Previous research has not found any relationship between positive affectivity and social support. | Descriptive Statistics Mean Std. Deviation N 3.3154 .92736 227 ABO PA 3.356 .6729 227...
Gain (V/V) R Setting Totals Averages Sample 1 Sample 2 Sample 3 4 ап 7.8 8.1 7.9 3 5.2 6.0 4.3 = 359.3 i=1 j=1 2 4.4 6.9 3.8 1 2.0 1.7 0.8 This is actual data from one of Joe Tritschler's audio engineering experiments. Use Analysis of Variance (ANOVA) to test the null hypothesis that the treatment means are equal at the a = 0.05 level of significance. Fill in the ANOVA table. Source of Variation Sum of Squares...
Gain (V/V) R Setting Totals Averages Sample 1 Sample 2 Sample 3 4 ап 7.8 8.1 7.9 3 5.2 6.0 4.3 = 359.3 i=1 j=1 2 4.4 6.9 3.8 1 2.0 1.7 0.8 This is actual data from one of Joe Tritschler's audio engineering experiments. Use Analysis of Variance (ANOVA) to test the null hypothesis that the treatment means are equal at the a = 0.05 level of significance. Fill in the ANOVA table. Source of Variation Sum of Squares...
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