ECMT1010 Lecture Notes - Lecture 10: The Intercept, Test Statistic, Confidence Interval

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browngrasshopper715

13 Aug 2018

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The generic equation of a regression line is: The regression line to predict y from x is not the same as the regression line to predict x from: a regression line is in the form: (cid:1844)(cid:1857)(cid:1871)(cid:1868)(cid:1867)(cid:1866)(cid:1871)(cid:1857) =(cid:1854)(cid:2868)+(cid:1854)(cid:2869) (cid:1831)(cid:1876)(cid:1868)(cid:1864)(cid:1853)(cid:1866)(cid:1853)(cid:1872)(cid:1867)(cid:1870)(cid:1877) The equation of the regression line is often called a prediction equation because we can use it to make predictions. We substitute the value of the explanatory variable into the prediction equation to calculate the predicted response. We seek the predicted temperature, given 140 chirps per minute. If the predicted values closely match the observed data values, the residuals will be small. The least squares line, also called the line of best fit is the line which minimises the sum of the squared residuals. Interpreting the slope and intercept of the regression line: Regression cautions: avoid trying to apply a regression line to predict values far from those that were used to create it, plot the data!

Related Questions

ECON 3050

Q24. The coefficient of determination (r²) is calculated as 0.49, then the correlation coefficient:

Cannot be determined without the data

Should be - 0.70 or 0.70

Should be 0.

Neither of the above

Q25. A regression line is used for all of the following except one. Which one is not a valid use of a regression line?

To estimate the average value of Y at a specified value of X.

To predict the value of Y for an individual, given that individual's X-value.

To estimate the change in Y for a one-unit change in X.

To determine if a change in X causes a change in Y.

Q26. Which choice is not an appropriate description of YË in a regression equation?

Estimated response

Predicted response

Estimated average response

Observed response

Q27. Which of the following is the best way to determine whether or not there is a statistically significant linear relationship between two quantitative variables?

Compute a regression line from a sample and see if the sample slope is 0.

Compute the correlation coefficient and see if it is greater than 0.5 or less than â0.5.

Conduct a test of the null hypothesis that the population slope is 0.

Conduct a test of the null hypothesis that the population intercept is 0.

Q28. There is no relationship between variables unless the data points lie in a straight line.

True

False

Q29. The sample regression analysis

Is the same as the population regression line

Is used to estimate the population regression line

Shows the true relation between dependent and independent variables

None of the above.

Q30. In regression, a dependent variable is sometimes called a predictor variable.

True

False

Q31. In a linear regression equation of the form y = a + bx, the intercept shows

The amount that y changes when x changes by one unit

The amount that x changes when y changes by one unit

The value of y when x is zero

The value of x when y is zero.

Q32. In a linear regression equation of y = a + bx, the slope b shows

Y / b

X / b

Y / X

X / Y

yellowturtle964

Econ 3050

7. When every member of the accessible population has an equal chance of being selected to participate in the study, the researcher is using:

a) Simple random sampling

b) Stratified random sampling

c) Convenience sampling

d) Purposive random sampling

8. A regression line has been found that has nearly all the points lying directly on the line, and only a few of them stray away from the line. Therefore, the standard error of the estimate is likely to be

Huge.

Small.

Undefined.

9. Correlation coefficient ranges from _______ to ____________.

a) - 1 to 0.

b) 0 to 1.

c) -1 to 1.

d) None of the above.

10. The correlation coefficient of determination is the:

a) Ratio of the explained variation to the total deviation.

b) Ratio of the unexplained deviation to the explained deviation.

c) Ratio of the unexplained deviation to the total variation.

d) Ratio of the explained variation to the total variation.

11. If the correlation coefficient r = 0.5 then the coefficient of determination is:

a) 0.10

b) 0.25

c) 1.00

d) 2.50

12. Which one of the following is NOT appropriate for studying the relationship between two quantitative variables?

Scatterplot

Bar chart

Correlation

Regression

13. In regression, an independent variable is sometimes called a response variable.

True

False

14. The simple linear regression equation can be written y = b₀ + b₁x. In the simple linear regression equation, the symbol y represents:

The average or predicted response

Estimated intercept

Estimated slope

Explanatory variable

mauvehyena239

Problem 1.

You are conducting a study on the price of houses in Los Angeles county, and studied data from n= 25 houses. Let the following variables denote your observations:

y^ = price of a house in thousands of dollars

x1= square footage

x2= distance in miles to nearest grocery store

x3 = a dummy variable that equals 1 if the house is in the top 50 state-

ranked school district and 0 otherwise.

x4= a dummy variable that equals 1 if the house is in Beverly Hills or Malibu

and 0 otherwise.

A) What do you predict would be the sign of each coefficient (bi) in the regression line? Briefly explain each.

B) Suppose b1=. 17 interpret the coefficient.

C) Suppose b4= 244.32. Interpret the coefficient

D) Suppose you run a restricted regression using x1, x2, and x4 yields R2 =

857. Furthermore, suppose the complete regression using x1, x2, x3 and x4 yields R2 = .772.

Which model do you think is better to use? Why?

E) Interpret R2 and R2 of the complete regression?

F) Why might the interaction term x1*x4 be useful to include in your

regression?

Thanks for your time

ECMT1010 Lecture Notes - Lecture 10: The Intercept, Test Statistic, Confidence Interval

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