Business Statistics Chapter 12 & 13

number of independent variables

"k" represents the n_________ o___ i____________ v__________ in the regression model.

dummy variable

A categorical independent variable with two levels is a what?

overall significance, MSR/MSE

An F-Test is a test for o________ s___________ of the regression model. The test statistic: (F-ration) is F=_____/______

goodness of fit in regression

Coefficient of determination (r-squared): "how well does the data fit the regression line?" is the test for g_______ o_ f___ i__ r____________.

scatter plot

Correlation vs. Regression: A s_________ p_______ can be used to show the relationship between two variables.

strength

Correlation vs. Regression: Correlation is only concerned with the s______ of the relationship.

correlation

Correlation vs. Regression: No casual effect is implied with c__________.

correlation analysis

Correlation vs. Regression: c__________ a___________ is used to measure the strength of the association (linear relationship) between two variables.

spurious correlation

Correlation vs. Regression: s_________ c__________ is when two unrelated variables correlate with each other, either by chance or by an unseen third factor. EG: shoe size and reading ability (3rd factor: age) EG2: Likelihood of dancing; likelihood of vomiting (3rd factor: alcohol consumption)

K, n-k-1

F-Stat follows an F distribution with ___ numerator and ____________ denominator degrees of freedom.

larger, more evidence

F-Test conclusion: The _________ the F-Ratio, the m_______ e___________ exists to reject Ho and prove that the relationship between x & y is statistically significant.

MSR/MSE (F-ratio)>Fa (a stands for alpha)

F-Test: Testing for over-all significance: Reject Ho if ______________

one-tailed

F-tests are o____-t______ tests.

Y, X

If r-squared = 30%: weaker linear relationship; a smaller portion of the variation in __ is explained by variation in ___.

no linear relationship, does not depend on x, no slope (none of the variation in Y is explained by variation is X)

If r-squared=0, then there is n__ l_________ r________, and the value of Y d_____ n_____ d______ o__ ___. The line has n__ s_______.

lower

If the p-value is _______ than alpha, then reject Ho.

y-intercept, x=0

In Y^ = bo+b1xi equation, "bo" is the _-________, the value of Y when ________(includes a symbol)

estimated, predicted

In Y^ = bo+b1xi, the y-hat is the _______ or p________ Y value for the observation i.

value of x, observation y

In equation Y^ = bo+b1xi, "Xi" is the v________ o_ __ for o_________ __.

slope of the line, y, x

In equation, Y^ = bo+b1xi, "b1" is the s_______ o__ t____ l_______, the change in __ divided by the change in ___

SSE/n-k-1

MSE is a ratio of what?

SSR/K

MSR is a ratio of what?

multiple regression

M__________ r___________: regression with two or more independent variables

unexplained variation

Measures of variation: SSE = error sum of squares. This is the u__________ v_________.

explained variation

Measures of variation: SSR = regression sum of squares. This is the e__________ v__________.

total variability

Measures of variation: SST = total sum of squares. This is the t_______ v________.

error sum of squares (Error Adj SS)

Measures of variation: What does SSE represent?

regression sum of squares (Regression Adj SS)

Measures of variation: What does SSR represent?

Total sum of squares (Total Adj SS)

Measures of variation: What does SST represent?

dependent variable, independent variable

Regression analysis is used to: Predict or explain the value of a d___________ v___________ based on the value of at least one i_____________ v__________.

overestimated, negative, underestimated, positive

Residual analysis: Points that have been o_____________ by the model will yield a n_________ residual value. (The estimated line is above the actual point.) Points that have been u_________ by the model yield a p__________ residual value. (The estimated line is below the actual point)

residual

Residual analysis: The r_______ is the difference between the point and the regression line.

difference between its observed and predicted value

Residual analysis: ei+yi-y^: The residual for each observation, ei, is the d_________ b________ i___ o__________ a____ p_________ v________.

simple linear regresion

S________ l__________ r_______: one independent variable

>

Testing for signficance: Reject Ho if (F-ratio) MSR/MSE __Fa

mean square due to regression, mean square due to error

The F-Ratio is a ratio of two variances: MSR represents what? MSE represents what?

x, y statistically significant

The F-Test in regression analysis answers the question: Is the relationship between the independent variable ___ and the dependent variable ___ s_________ s________?

over-all

The F-test tests for ____-___ significance (in linear relationship)

smaller

The __________ the p-value, you have ample evidence to reject Ho.

linear, 0 and 1, stronger, negative

The coefficient of determination (r-squared) measures the strength of the l______ relationship between x and y. It's the test of goodness of fit in regression (How well does the data fit the regression line?). Its value is between _(#)_ and _(#)___. The higher the percentage, the s_________ the linear relationship between x and y. It will never be n________.

percent of the total variability of y (measured by SST) that is explained by the independent variable (measured by SSR).

The coefficient of determination is the p________ o_ t____ t_________ v__________ o__ __ t______ i__ e_________ b___ t___ i__________ v________. It is also referred to as r-squared. The ratio is SSR/SST.

SSR/SST (regression sum of squares/total sum of squares)

The r-squared ration is: r-squared = ___________________

estimate

The simple linear regression equation provides an e__________ of the population regression line. Y^ = bo+b1xi

independent variable (X)

The variable used to predict or explain the dependent variable

dependent variable (Y)

The variable we wish to predict

SST = SSR+SSE

What is the equation for total variation (made up of two parts)?

F-test

Which test is a one-tailed test?

T-test (look up half of alpha)

Which test is a two-tailed test?

T-test, p-value test

Which test(s) tests for individual significance

change in the mean value of Y as a result of a one-unit increase in X

Y^ = bo+b1xi: "b1" (slope) is the estimated c_________ i___ t_____ m________ v_________ o__ __ a__ a r_________ o__ a o______-u________ i_________ i__ __. (see slide 4)

coefficient of determination

r^2 (r-squared) is the what?

0 or 1

dummy variables (categorical independent variables with two levels like yes or no) are coded as what?

negative, positive, no difference

dummy variables: If the coefficient has a negative value, the presence of the qualitative variable has a __________ impact on the model. If the coefficient has a positive value, the presence of the qualitative variable has a __________ impact on the model. If the coefficient is 0 (or near 0), there is n___ d_________ in the presence or absence of the qualitative variables in the model.