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Online Homework assignment for chapter 14 on CONNECT ...

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CH14 Saturday, April 20, 2019 12:37 PM

quizlet we specify the alternative hypothesis as ha:p coefficient of determination formula ^ | |

quizlet if the sample regression equation is y^ = 15 + 5x which of the The following line crosses is the the y axis at y=15 correct interpretation of the estimated intercept

Reponse variable symbol

Y

If one variable decreases as the other variable decreases, the two variables Positive have that type of relationship? 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 nfreedom. In an attempt to predict a single response variable y, three models areModel estimated. The 1 standard error of the estimate for Model 1 equals 10, for Model 2 equals 100, and for Model 3 equals 1000. According to the standard error of the estimate, which model provides the best fit? If the sample regression equation is to be yhat = 10+2x1-3x2, what is yhat predicted = 10 + 2(4) - 3(1) = 15 valueof y when x1 = 4 and x2 = 1? If two variables X1 and Y1 have a covariance of 25 and two other variables Each X2 setand shows Y2 a positive linear relationship. have a covariance of 65, what conclusion can we draw about the relationships? since the p-value exceeds 0.05. When testing whether the correlation coefficient differs from zero, theNo, value of the test statistic is t20=1.95 with a corresponding p-value of 0.0653. At the 5% significance level, can you conclude that the correlation coefficient differs from zero? When conducting a hypothesis test, we determine

Whether the sample data support the alternative hypothesis.

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

The scatterplot can be used to assess the linearity of the relation

Given the sample regression equation yhat=15+3x, which of the following 1. yhat=15+3(1)=18; is the value y-yhat=19-18=1. of the residual at the point (1,19) The common approach to fitting a line to sample data in a scatterplot isminimize to the value of the sum of the squared residuals.

In regression, if Multiple R equals 0.80, then R2 equals

0.64. 0.80x0.80 = 0.64

68of ten college What values will be considered Outliers in the following data set of ages students? 18,18,20,19,22,21,25,23,28,68. by 3 units. Consider the following sample regression equation: yhat=17-3x1+3x2.Decreased What will be the average change in the estimated value of y, given a unit change in x1(holding x2 constant)? If the correlation between the response variable and the explanatory variable May be negative is sufficiently low, then adjusted R2 In a study, the estimated linear regression equation is given as yhat=20-3x. The slope Interpret is negative, indicating a negative linear relationship. the estimated slope coefficient. What is the difference between correlation and causation?

Correlation means that two variables are related, but causation m the other to happen.

Which of the following is a goodness-of-fit measure?

Coefficient and determination.

The standard error of the estimate is the standard deviation of the

Residuals

If the sample regression equation is yhat=15+5x, which of the following The is line the crosses correct the y-axis at y=15. interpretation of 15? Consider the simple linear regression model: y=B0 + B1x +E. What is the notation for the intercept?

B0

In a simple linear regression model, if all of the data points fall on the sample 1 regression line, then the coefficient of determination is If rxy = 0.83, then we conclude that X and Y have relatively

strong, positive linear relationship.

In a simple linear regression model, if all of the data points fall on the sample 0 regression line, then the standard error of the estimate is In a simple linear regression model, if all of the data points fall on the sample When we test if two variables are negatively linearly related. regression line, then the standard error of the estimate is What type of relationship exists between two variables if as one increases, Positive the other increases? If the sample regression equation is found to be yhat=30+5x, what is the 5 estimate for the slope coefficient B1? If the sample regression equation is found to be yhat+10-2x1-3x2, what -1 is the predicted value of y when x1=4 and x2=1? Suppose that the slope parameter in a simple linear regression model Positive is B1=3.52. linear relationship. What does this possibly suggest about the nature of the relationship between x and y? One limitation of correlation analysis is that it

One limitation of correlation analysis is that it

The goodness-of-fit measure that quantifies the proportion of the variation coefficient in the of determination. response variable that is explained by the sample regression equation is the How many explanatory variables does a simple linear regression model One have? The graph used to show the relationship between two variables is the scatterplot. Unlike R2, adjusted R2 can be used to compare regression models withdifferent numbers of explanatory variables. The standard error of the estimate can assume which of the following values? Between zero and infinity. The R2 of a multiple regression of y as a function of x measures the Consider the simple linear regression model: y=B0+B1x+E. What is the notation for the slope coefficient?

percentage variability of y that is explained by the variability of x B1

In hypothesis tests about the population correlation coefficient, the alternative linearly related. hypothesis of not equal to zero is used when testing whether two variables are Consider the following sample regression equation: yhat=17+5x1+3x2. ForInterpret a unit increase the in x1, the average value of y will increase by 5 value 5. constant. The estimated linear regression equation is yhat=-15+3x. Interpret the When intercept. x=0, the predicted value of y is -15. If the sample regression equation is found to be yhat=20+10x, what is50 the Predicted value of y when x=3? The coefficient of determination can assume which of the following values? Between zero and one. Consider the simple linear regression model: y=B0+B1x+E. What is the notation for the random error term?

E

Which of the following is NOT true of the standard error of the estimate? It can take on negative values. Given the sample regression equation yhat=15+3x, which of the following 10. yhat=15+3(0)=15; is the value y-yhat=25-15=10. of the residual at the point (0,25). Which of the following is another name for R2?

Coefficient of determination.

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

For which of the following situations is a simple linear regression model The appropriate? response variable y is influenced by one explanatory variabl When is the multiple regression model used? In regression analysis, the explanatory variable is also called the

When the researcher believes that two or more explanatory varia response variable. Independent variable.

When the response variable is uniquely determined by the explanatorydeterministic. variable, the relationship is Unlike R2, adjusted R2 accounts for

The sample size and the number of response variables.

Which of the following is a possible advantage of using multiple tools to Tojudge avoidthe the risk of using the wrong model. validity of a regression model? The residual e represents In regression analysis, the response variable is also called the

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

SST respresents

The total variation in y.

In regression model, the residual e is calculated as

y-yhat.

What sample correlation coefficient who show the strongest association Closet between to -1 Xor 1 and Y? Which of the following is NOT true of the standard error of the estimate? It can take on negative values Which of the following is true of the standard error of the estimate?

-Theoretically, its value has no predefined upper limit -it is a measure of the accuracy of the regression model -It is based on the squared deviations between the actual and pre the response variable

What is true concerning correlation analysis?

-The correlation coefficient captures only a linear relationship -the correlation coefficient may not be a reliable measure when o in one or both of the variables -correlation does not imply causation

Goodness-of-fit measures:

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

In hypothesis tests about the population correlation coefficient, the alternative linearly related hypothesis of not equal to zero is used when testing whether two variables are ____________ In simple linear regression, a downward sloping trend line suggests which A negative of the linear relationship between x and y following? What type of relationship exists between two variables if as one increases, Positive the other increases? What best defines the rejection region of a test?

The set of values of a test statistic for which the null hypothesis i

The coefficient of determination can assume what value?

Between zero and one

If the sample regression equation is y (hat)= 15/5x, which is the correct For interpretation every unit increase in x, y will decrease, on average, by 5 unit of the estimates slope coefficient? How many explanatory variables does a simple linear regression model One have? T/F: The scatterplot is a graphical tool where each point in the plot represents True a pair of observed values of the two variables The goodness-of-fit measure that quantifies the proportion of the variation coefficient in the of determination response variable that is explained by the sample regression equation is the What is the notation for the random error term? The residual e represents y(hat) = 20 - 3x. Interpret the estimated slope coefficient:

E The difference between an observed and predicted value of the re a given value of the explanatory variable The slope if negative, indicating a negative linear relationship

What values can the standard error of the estimate, s, assume?

0 0 what is the relationship?

positive linear relationship

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

negative linear relationship

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

the predicted value of the response variable given a specified va explanatory variable x

residual e

the difference between the observed and the predicted values − of y(hat) ,

On a scatterplot for simple linear regression model, where do x and y go? y on vertical axis, x on horizontal axis implying that x influences the variation in y To estimate the parameters β0 and β1 we use what? OLS method (ordinary least squares)

the method of least squares (ordinary least squares (OLS)) produces the straight line that is "closest" to the data by finding w minimized. SSE is the sum of the squared differences between the and their predicted values y(hat) OR the sum of the squared dista regression equation

T/F: By restricting the number of explanatory variables to one in the simple True linear regression model, we reduce potential usefulness of the model Multiple linear regression model allows us to study what?

how the response variable is influenced by two or more explanat

T/F: In multiple linear regression for the sample regression equation, biTrue; measures the bi represents the partial influence of xi on y(hat) change in the predicted value of the response variable y(hat) given a unit increase in the associated explanatory variable xi, holding all other explanatory variables constant In order to select the preferred model (multiple or singular) we need togoodness-of-fit examine measures what? The standard error of the estimate, Se, is what?

The positive square root of Se^2

How to determine the better fit to a model

the smaller Se implies a better fit to the model

Se can assume what values

0 to infinity but the closer to 0, better the model fits

Why do we use the multiple regression model instead of the simple regression model? We add explanatory variables to increase model's When to use Standard Error of the Estimate

-When we are comparing various models -model with smaller Se is better fit

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

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

Interpret an R^2 of .72

72% of the sample variation in the response variable is explained regression equation (stronger fit) Other factors not included in model account for remaining 28% of

What does the value of R^2 fall between?

0 and 1 Closer to 1= stronger fit Closer to 0= weaker fit (same with R)

Multiple R

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

Adjusted R^2

-used to compare competing linear regression models with differe explanatory variables -higher the value, better the model

Summarize the three conditions that must be checked before carrying1.) outrandom significance sample? tests: 2.) normal? 3.) stating the null hypothesis and alternative hypothesis State the general form of the "test statistic".

(statistic-parameter) ----------------------(standard deviation of statistic)

What does the test statistic measure?

measures how far a sample statistic diverges from what we woul hypothesis Ho were true in standardized units

1.) State: Describe the four step process for significance tests. Explain what is required at what each hypotheses do you want to test, and at what signif define any parameter used. step. 1.) State

2.) Plan: choose the appropriate inference method. check conditio

2.) Plan 3.) Do

3.) Do: If conditions are met, perform calculations. -compute the test statistics -find the p-value

4.) Conclude

4.) Conclude: interpret the results of your test in the context of th

What test statistic is used when testing for a population proportion?

1-sample z test for proportion

What test statistic is used when testing for a population proportion?

1-sample z test for proportion

1.)possible Choose... Summarize the one-sample z test for a proportion and sketch the three Haa'sSRS of size n from a large population that contains proportion p of successes 1.) Choose... 2.) To test... the hypothesis Ho:P=Po, compute the z statistic −p0√p0(1−p0)n. z=ˆp 2.) To test... 3.) Find... 4.) Use this test... 5.) If Normality is not met…

3.) Find... the p-value by calculating the probability of getting a z s or larger in the direction specified by alternative hypothesis 4.) Use this test... only when the expected numbers of successes a and n(1-Po) are both greater than or equal to 10 and the populatio as large as the sample 5.) If Normality is not met... or if the population is less than 10x as sample, other procedures should be used

What happens when the data doesn't support Ha?

if the data doesn't support Ha, then we fail to reject the null hypo continue with the test

If asked to carry out a significance test and there is no α provided, what assume is α=0.05 recommended? Can you use confidence intervals to decide between two hypotheses? -yes What is the advantage to using confidence intervals for this purpose? -it tells us if a hypothesis is contained within a population Why don't we always use confidence intervals? they are more useful for 2 sided tests Which of the following identifies the range for a correlation coefficient? None of the above The correlation coefficient can range from -1 to 1. A correlation coefficient r = -0.85 could indicate a:

Very strong negative linear relationship.

The following scatterplot implies that the relationship between the twoStrong variables and xpositive. and y is: The scatterplot is increasing, going from left to right. The following scatterplot implies that the relationship between the twoStrong variables and xNegative and y is: The scatterplot is going left to right and decreasing. Which of the following statements is least accurate concerning correlation Theanalysis? correlation coefficient describes both the direction and stren relationship between two variables only if the two variables have measurement. Simple linear regression analysis differs from multiple regression analysis Simple in that: linear regression uses only one explanatory variable. A regression equation was estimated as ÿ=100+.05X1 . If X1= 20, the-90 predicted value of y is: -100+.5(20)=-90 What is the name of the variable that's used to predict another variable? Explanatory Consider the following simple linear regression model: y=Bo+B1+Ę. The Y response variable is: Consider the following simple linear explanatory model: y=Bo+B1X+Ę.XThe explanatory variable is: Consider the following simple linear regression model: y=Bo+B1X+Ę. The E random error term is: Consider the following simple linear regression model: y=Bo+B1X+Ę. β0 the and unknown β1 are parameters In the sample regression equation y=Bo+B1X, what is Y?

The predicted value of y, given a specific x value

Given the augmented Phillips model: , y=Bo+B1X1+B2X2+Ę where y = actual rate of Rate Actual Inflation inflation (%), x1 = unemployment rate (%), and x2 = anticipated inflation rate (%). The response variable(s) in this model is(are) the: Unemployment Given the augmented Phillips model: , y=Bo+B1X1+B2X2+Ę where y = actual rate of rate and anticipated inflation rate inflation (%), x1 = unemployment rate (%), and x2 = anticipated inflation rate (%). The explanatory variable(s) in this model is(are) the: R-Rf The capital asset pricing model is given by: R-Rf=a+B(Rm-Rf)+Ę , where Rm = expected return on the market, Rf = risk-free market return, and R = expected return on a stock or portfolio of interest. The response variable in this model is: The capital asset pricing model is given by: R-Rf=a+B(Rm-Rf)+Ę , where Rm = expected Rm-Rf return on the market, Rf = risk-free market return, and R = expected return on a stock or portfolio of interest. The explanatory variable in this model is: Consider the sample regression equation: Ÿi=10-5xi , with an R2 value-.81 of 0.65. What is the value of the correlation coefficient between x and y? r = sqrt(R2). Consider the sample regression equation: ÿi=100+10Xi , with an R2 value 0.90of 0.81. What is the value of the correlation coefficient between x and y?

What is the value of the correlation coefficient between x and y? In a simple linear regression model, if the plots on a scatter diagram lie 0 on a straight line, what is the standard error of the estimate? In a simple linear regression model, if the plots on a scatter diagram lie +1 on a straight line, what is the coefficient of determination? Calculate value of R2 given the ANOVA portion of the regression outputR2=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-va

The standard error of the estimate measures

the standard deviation of the residuals.