# Two variable regression

A random sample of size five, for two variables X and Y has been collected. The values for the data are:
$\begin{tabular}{lll} &~X~&~Y~\\ 1~&~7~&~15~\\ 2~&~8~&~13~\\ 3~&~10~&~10~\\ 4~&~12~&~7~\\ 5~&~13~&~5~\\ \end{tabular}$
The sample slope coefficient from a regression of Y on X is:

Using the data above, what is the estimated value of the intercept.

Using the data above, what are the estimated values for the residuals:

In regression analysis, if the independent variable is measured in kilograms, the dependent
variable:

When the error terms are independent, which of the following characteristics are the residuals likely to possess?

The RSS can never be :

When the error terms have a constant variance, a plot of the residuals versus the independent variable x has a pattern that:

All of the following are assumptions of the error terms in the simple linear regression model except

A fitted least squares regression line:

In a regression analysis if $~R^2~=~1~$, then:

Examine the following results which are based on a fictitious model
$\begin{tabular}{lllll} Model~1~~&~cor(x,y)~&~~R^2~&~\bar{R}^2~&~\hat{\sigma}~\\ ~&~0.863~&~0.849~&~0.850~&~13.877~\\ \end{tabular}$
Which of the following statements can we NOT say?

In a sample of 100 observations, the sample correlation between two variables, y and x, was found to be 0.72. Based on this data, the least squares regression line was computed to be $y=7-3.4x.$
This means that the percentage of observed variation in y explained by a linear relationship with x is:

The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study:
$y=~-0.0127~+~0.0180x~$
The above equation implies that:

A regression analysis between sales (in £1000) and price (in pounds) resulted in the following
equation:
$~ ~y~=~50,000~-~8.0X~ ~$
The above equation implies that an:

Regression analysis was applied to return rates of sparrowhawk colonies. Regression analysis was
used to study the relationship between return rate (x: % of birds that return to the colony in a given year) and immigration rate (y: % of new adults that join the colony per year). The following regression equation was obtained.
$y~=~31.9~-~0.34x$
Based on the above estimated regression equation, if the return rate were to decrease by 10% the rate of immigration to the colony would:

• multiplying y by 100
• Multiplying ln(y) by 100
• multiplying x by 100
• multiplying ln(y) and ln(x) by 100
• Multiplying ln(x) by 100

Which of the follow are correct definitions of the standard error of the regression.

Consider the following model:
$~ln(y_i)=3.21+0.22*D_i+\hat{\epsilon_i}~$, where $~D_i=1~$ if female, 0 otherwise . Which of the following is the correct interpretation of the coefficient on $~D_i~$?

Consider the following model:
$~ln(y_i)=3.21+0.12*x_i+\hat{\epsilon_i}~$. Which of the following is the correct interpretation of the coefficient on $~x_i~$?

Consider the following model, which was estimated on 63 observations
$\begin{tabular}{rlll} y_i=~&~~6.23+~&~~1.36x_i+~&~\hat{\epsilon_i}~\\ &~(2.61)~&~(0.16)~&~\\ \end{tabular}$
Standard errors in parentheses. Test the hypothesis that the slope coefficient is unity.

Consider the following model:
$~ln(y_i)=3.21+0.12*ln(x_i)+\hat{\epsilon_i}~$. Which of the following is the correct interpretation of the coefficient on $~ln(x_i)~$?

Consider the following model, which was estimated on 43 observations
$\begin{tabular}{rlll} y_i=~&~~6.23+~&~~1.36x_i+~&~\hat{\epsilon_i}~\\ &~(2.61)~&~(0.16)~&~\\ \end{tabular}$
Standard errors in parentheses. What is the critical value of the test statistic if you are testing the hypothesis that the slope coefficient is unity at the 5/% significance level.

Consider the following model, which was estimated on 23 observations
$\begin{tabular}{rlll} y_i=~&~~6.23+~&~~1.36x_i+~&~\hat{\epsilon_i}~\\ &~(2.61)~&~(0.16)~&~\\ \end{tabular}$
Standard errors in parentheses. Calculate 90% confidence interval on the slope coefficient (2 decimal places).

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