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# Business Statistics 222 Exam 1

Ch. 12, 13, 14
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The F Distribution ranges between...
0 and ∞
If the computed value of F is .99 and the critical value is 3.89, we would NOT reject the null hypothesis.
TRUE
If the F value is > the critical value, would we reject the null?
Yes
If the F value is < the critical value, would we reject the null?
No. We would ACCEPT the null.
3. In an ANOVA - Does rejection of the null identify which means differ?
No.
TRUE or FALSE?
The alternative hypothesis for ANOVA states that not all the means are equal.
TRUE
When blocking effect is included in an ANOVA, the result is ...
A smaller set of squares.
One-way blocked analysis of variance (ANOVA) is used to...
Test the null hypothesis that multiple population means are all equal, allowing for block effects.
5. If the confidence interval is 0 between a pair of means - do they differ?
No.
TRUE or FALSE?
If a confidence interval for the difference between a pair of treatment means includes 0, then there is no difference in the pair of treatment means.
TRUE
6. What is an F statistic?
A ratio of two variances.
In an ANOVA how do you calculate DOF (Degrees of Freedom) for the numerator?
To calculate the DOF for the Numerator subtract the # of treatments (# of samples) by 1.
In an ANOVA how do you calculate DOF (Degrees of Freedom) for the denominator?
To calculate the DOF for the Denominator, take total sample size (sum of each of the sample sizes) and subtract it by the number of treatments (# of samples).
Given the following Analysis of Variance table for three treatments each with six observations,
TREATMENTS 1116
ERROR 1068
TOTAL 2184

Calculate the DOF for the Numerator.
Since there are 3 treatments, the degree of freedom associated with the numerator is 2 (3-1 = 2).
Given the following Analysis of Variance table for three treatments each with six observations,
TREATMENTS 1116
ERROR 1068
TOTAL 2184

Calculate the DOF for the Denominator.
The degree of freedom associated with the denominator is 15 (3x6 = 18 - 3 = 15)
Calculate the critical value of F at the 5% level of significance for the DOF associated with the Numerator = 2 and Denominator = 15
Use the F Distribution Table (Appendix B) at the 5% Level of Significance.
Find the Degrees of Freedom for the Numerator (2) and scroll down to the Degrees of Freedom for the Denominator (15) these cross at 3.68. The theoretical F value is 3.68
Given the following Analysis of Variance table for three treatments each with six observations,
TREATMENTS 1116
ERROR 1068
TOTAL 2184

What is the mean square for treatments?
Mean Square for Treatments = Sum of Square Error for Treatment / Degrees of Freedom associated with treatment.
= 1116 / 2 = 558
Given the following Analysis of Variance table for three treatments each with six observations,
TREATMENTS 1116
ERROR 1068
TOTAL 2184

What is the computed value of F?
Do you reject the null?
To Determine the computed F value:
• Compute the mean square error for both for treatment and error. (We know that the latter is 558).
• The mean square for error is 1068/15 = 71.2
• Thus, the computed F value which is the ratio of the mean square error for treatment to mean square error for random variation = 558/71.2 = 7.84

Reject H0 - there is a difference in treatment means
Since the critical F value for 2 and 15 degrees of freedom is 3.68 and the computed F value is 7.84, the hypothesis that the means are equal should be rejected.
What is a scatter diagram?
A chart that portrays the relationship between two variables.
13. What does the sign (- or +) mean regarding correlation?
The sign of the correlation coefficient (+ , -) defines the direction of the relationship, either positive or negative. A positive correlation coefficient means that as the value of one variable increases, the value of the other variable increases; as one decreases the other decreases. A negative correlation coefficient indicates that as one variable increases, the other decreases, and vice-versa.
TRUE or FALSE?
The coefficient of correlation, r, close to 0 (says, 0.08) shows that the relationship between two variables is quite weak.
TRUE
TRUE or FALSE
If the coefficient of determination is .90, the coefficient of correlation is .81
FALSE
An assumption of linear regression is ?
Is that the Y values are statistically dependent on the X values.
Is that for each value of X there is a group of Y values that is normally distributed.
The means of these normal distributions of Y values all lie on the straight line of regression
The standard deviations of these normal distributions are equal.
16. A straight line going through the points on a scatter chart is?
A regression line
What is an independent variable?
A variable (often denoted by x) whose variation does not depend on that of another.
What does a coefficient of correlation of .70 infer?
Coefficient of determination is 0.49
Pearson's r can range from...
-1 to 1
An r of -1 indicates ...
A perfect negative linear relationship between variables.
An r of 0 indicates ...
no linear relationship between variables
an r of 1 indicates ...
a perfect positive relationship between variables
TRUE or FALSE
A coefficient of correlation, r close to 0 (say, 0.08) shows that the relationship b/w two variables is quite weak.
TRUE
The correlation = 1 means?
An r of 1 indicates a perfect positive relationship between variables.
What is the range for correlation?
-1 to 1
A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is .60, then what is the computed value of the test statistic?
=.60O(25-2)/O(1r^2)=3.60
If the regression equation is Y = 1202 + 1133X and x = 3 then what is Y?
Y = 1202 + 1133(3) --> Y = 4601
Suppose the least squares regression equation is Y = 1202 + 1,133X. When X = 3, what is Y?
Plug the X value in and you get = 1202 + 1133 (3) = 4601
What are the assumptions of linear regression?
1. For each value of X, there is a group of Y values which is normally distributed
2. The means of these normal distributions of Y values all lie on the straight line of regression
3. The standard deviation of these normal distributions are equal
Assume the least squares equation is Y = 10 + 20X, what does the value of 10 in the equation indicate?
Y INTERCEPT
What is multiple regression used for?
When two or more independent variables are used to predict a value of a single dependent variable.
TRUE or FALSE?
The coefficient of multiple determination reports the strength of the association between a dependent variable and a set of independent variables.
TRUE
The coefficient of multiple determination is 0.81, what percent of variation is not explained?
19%
29. What is a multiple correlation coefficient?
An estimate of the combined influence of two or more variables on the observed (dependent) variable.
31. Can a correlation matrix help assess multicollinearity?
A correlation matrix can be used to assess multicollinearity between independent variables.
32. What is used to test the global hypothesis in multiple regression?
F-statistic
TRUE or FALSE?
To test the global hypothesis in multiple regression analysis, a t-statistic is used.
FALSE
TRUE or FALSE
Autocorrelation often happens when data has been collected over periods of time.
TRUE
TRUE or FALSE
In multiple regression analysis, a residual is the difference between the value of a dependent variable, Y, and it's predicted value, Y.
TRUE
What is the value range for R2?
0% to + 100% inclusive
What does the multiple standard error of estimate measure?
The "error" or variability in predicting Y
If the correlation between the two independent variables of a regression analysis is 0.11 and each independent variable is highly correlated to the dependent variable, what does this indicate?
Both independent variables should be used to predict the dependent variable.
What can we conclude if the net regression coefficients in the population are not significantly different from zero?
No relationship exists between the dependent variable and any of the independent variables.
For a unit change in the first independent variable with other things being held constant, what change can be expected in the dependent variable in the multiple regression equation Y = 5.2 + 6.3X1 7.1X2?
+6.3
What is a correlation matrix?
A branch of applied mathematics concerned with the collection and interpretation of quantitative data and the use of probability theory to estimate population parameters.