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the the following simple linear regression model

The the following simple linear regression model

lOMoARcPSD|16107334

Saturday, April 20, 201912:37 PM

quizlet we specify the alternative hypothesis as ha:p<0 when we want to test if Two variables are negatively linearly related

quizlet if the sample regression equation is y^ = 15 + 5x which of the correct interpretation of the estimated intercept

following is the The line crosses the y axis at y=15

ables have that
Which of the following statements is true about the test of Ho : Pxy = 0?The test statistic is assumed to follow the tdf distribution with n-2 de freedom.
estimated. The
ls 100, and for
which model

If the sample regression equation is to be yhat = 10+2x1-3x2, what is valueof y when x1 = 4 and x2 = 1?

predicted yhat = 10 + 2(4) - 3(1) = 15

If two variables X1 and Y1 have a covariance of 25 and two other varia have a covariance of 65, what conclusion can we draw about the relati
When testing whether the correlation coefcient difers from zero, the test statistic is t20=1.95 with a corresponding p-value of 0.0653. At th level, can you conclude that the correlation coefcient difers from zer value of the No, since the p-value exceeds 0.05. e 5% signifcance
o?

In evaluating a regression model, why is a scatterplot a useful tool?

The scatterplot can be used to assess the linearity of the relationship.

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For which of the following situations is a simple linear regression model appropriate? The response variable y is influenced by one explanatory variable.

When the response variable is uniquely determined by the explanatory relationship is

variable, the

o judge the To avoid the risk of using the wrong model.

The difference between an observed and predicted value of the respo a given value of the explanatory variable.

In regression analysis, the response variable is also called the

y-yhat.

What sample correlation coefcient who show the strongest associatio and Y?

n between X Closet to -1 or 1
Which of the following is NOT true of the standard error of the estimat e?It can take on negative values

Goodness-of-fit measures:

-the standard error of the estimate
-the coefficient of determination
-the adjusted coefficient of determination

ich of the A negative linear relationship between x and y

What type of relationship exists between two variables if as one increa increases?

ses, the other
The set of values of a test statistic for which the null hypothesis is rej

t interpretation For every unit increase in x, y will decrease, on average, by 5 units

How many explanatory variables does a simple linear regression mode

l have?

resents a pair
The goodness-of-ft measure that quantifes the proportion of the varia response variable that is explained by the sample regression equation

E

The residual e represents

0 <_ s < infinity

The standard error of the estimate can assume what value?

use certain variables that impact the response variable are not included i

What best defines a test statistic in a hypothesis test?

a variable upon which the decision in hypothesis testing is based

ses, the other

has no predefined upper limit, it is hard to interpret in isolation

In a regression model, the Multiple R is the

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In E(y) = β0 + β1x, when β1 = 0 what is the relationship?

no linear relationship

In the sample regression equation: y(hat)= b0 + b1x, y(hat) is

the predicted value of the response variable given a specifed value explanatory variable x

implying that x influences the variation in y

To estimate the parameters β0 and β1 we use what?

mple linear

Multiple linear regression model allows us to study what?

how the response variable is influenced by two or more explanatory v

T/F: In multiple linear regression for the sample regression equation, bi change in the predicted value of the response variable y(hat) given a u the associated explanatory variable xi, holding all other explanatory va measures the True; bi represents the partial influence of xi on y(hat)u nit increase in
riables constant

How to determine the better fit to a model

the smaller Se implies a better fit to the model

Why do we use the multiple regression model instead of the simple re gression model? We add explanatory variables to increase model's use

Which is easier to interpret and why? R^2 or Se?

R^2 because it has both lower and upper bounds that make its interp intuitive

Multiple R

R^2 is the square of multiple R
Multiple R is the square root of R^2

2.) normal?

3.) stating the null hypothesis and alternative hypothesis

Describe the four step process for signifcance tests. Explain what is re step.

1.) State
2.) Plan
3.) Do
4.) Conclude

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e on a straight
e on a straight
Calculate value of R2 given the ANOVA portion of the regression outpu tR2=SSR/SST
Which of the following is not true of the standard error of the estimate ?It can take on negative values.

The standard error of the estimate measures

the variability of the observed y-values around the predicted y-value

The standard error of the estimate measures

Percent variability of y that is explained by the variability of x1 and x
a simple linear Indicates whether the slope of the regression line is positive or negat

me response Lower standard error of the estimate and a higher adjusted coefcien

at would determination.

adjusted R2

In the estimation of a multiple regression model with two explanatory 20 observations, SSE=550 and SST=1000 . What is the value of R2?

variables and
R2=1-SSE/SST
In the estimation of a multiple regression model with four explanatory 25 observations, SSE=660 and SST=1000 . The value of adjusted R2 is
Consider the following simple linear regression model: y=Bo+B1X+Ę . determining whether x signifcantly infuences y, the null hypothesis ta

Consider the following simple linear regression model: y=Bo+B1X+Ę . determining whether there is a positive linear relationship between x a alternative hypothesis takes the form

When Ha:B1>0

Excel and virtually all other statistical packages report the p-value

for a two-tailed test that assesses whether the regression coefcient zero.

Since the p-value is 0.0028, which is less than α = 0.05, we can conc one explanatory variable is signifcantly related to the response varia

Given the following portion of regression results, what is the value of t statistic?

he F2,20 test
F(2,20)=MSR/MSE
The accompanying table shows the regression results when estimating signifcance level, which explanatory variable(s) is(are) individually sig

. At the 5% Since the p-values for the slope coefcients attached to x1 and x2 ar

nifcant? signifcance level of 0.05, these two variables are both individually si

The accompanying table shows the regression results when estimating signifcance level, which explanatory variable(s) is(are) individually sig

used to study if

atistic for the

In regression, the two types of interval estimates concerning y are call ed: confidence interval and prediction interval.

For a given confdence level, the prediction interval is always wider tha confidence interval becau

n the The prediction interval is for a particular value of y rather than for th

In regression, multicollinea

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