Linear Regression Inference and Transformations Review

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. We collected data on the appraised market values x and the actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data. The equation of the least-squares regression line for predicting selling price from appraised value is

• $\overline{price}=79.49+0.1126\left(appraised\ value\right)$

• $\overline{price}=0.1126+1.0466\left(appraised\ value\right)$

• $\overline{price}=127.27+1.0466\left(appraised\ value\right)$

• $\overline{price}=1.0466+127.27\left(appraised\ value\right)$

• $\overline{price}=1.0466+69.7299\left(appraised\ value\right)$

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. We collected data on the appraised market values x and the actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data. The slope beta of the population regression line describes

• the exact increase in the selling price of an individual unit when its appraised value increases by $1000.

• the average increase in the appraised value in a population of units when selling prices increases by $1000.

• the average increase in selling prices in a population of units when appraised value increases by $1000.

• the average increase in the appraised value in the sample of units when selling price increases by $1000.

• the average increase in selling price in the sample of units when the appraised value increases by $1000.

Tags

CCSS.HSS.ID.C.7

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. We collected data on the appraised market values x and the actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data. Is there convincing evidence that selling prices increases as appraised value increases? To answer this question, test the hypotheses

• $H_0:\beta=0\ versus\ H_a:\beta>0$

• $H_0:\beta=0\ versus\ H_a:\beta<0$

• $H_0:\beta=0\ versus\ H_a:\beta\ne0$

• $H_0:\beta>0\ versus\ H_a:\beta=0$

• $H_0:\beta=1\ versus\ H_a:\beta>1$

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. We collected data on the appraised market values x and the actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data. Which of the following is the best interpretation for the value 0.1126 in the computer output?

• For each increase of $1000 in appraised value, the average selling price increases by about 0.1126.

• When using this model to predict selling price, the predictions will typically be off by about 0.1126.

• 11.26% of the variation in selling price is accounted for by the linear relationship between selling price and appraised value.

• There is a weak, positive linear relationship between selling price and appraised value.

• In repeated samples of size 16, the sample slope will typically vary from the population slope by about 0.1126.

Tags

CCSS.HSS.ID.C.7

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. We collected data on the appraised market values x and the actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data. A 95% confidence interval for the population slope beta is

• $1.0466\pm1.046$

• $1.0466\pm0.2415$

• $1.0466\pm0.2387$

• $1.0466\pm0.2207$

• $1.0466\pm0.2400$

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.C.7

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. We collected data on the appraised market values x and the actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data. Which of the following would have resulted in a violation of the conditions for inference?

• If the entire sample was selected from one neighborhood

• If the sample size was cut in half

• If the scatterplot x= appraised value and y= selling price did not show a perfect linear relationship

• If the histogram of selling prices had an outlier

• If the standard deviation of appraised values was different from the standard deviation of selling prices

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.A.3

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

Suppose that the relationship between a response variable y and an explanatory variable x is modeled by y=2.7(0.316)^x. Which of the following scatterplots would approximately follow a straight line?

• A plot of y against x

• A plot of y against log x

• A plot of log y against x

• A plot of log y again log x

• A plot of the square root of y against x

Tags

CCSS.HSF.LE.A.2

Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If you have studied physics, then you probably know that the theoretical relationship between the variables is distance = 490(time)². A scatterplot of the students' data showed a clear curved pattern. At 0.68 seconds after release, the ball had fallen 220.4 centimeters. How much more or less did the ball fall than the theoretical model predicts?

• More by 226.576 centimeters

• More by 6.176 centimeters

• No more and no less

• Less by 226.576 centimeters

• Less by 6.176 centimeters

Tags

CCSS.HSA.REI.B.4

CCSS.HSA.REI.D.11

CCSS.HSA.SSE.A.1

A scatterplot of x = Super Bowl and y = cost of a 30-second advertisement on the Super Bowl broadcast (in dollars) shows a strong, positive, nonlinear association. A scatterplot of ln(cost) versus Super Bowl number is roughly linear. The least squares regression line for this association is predicted ln(cost)=10.97+0.0971(Super Bowl number). Predict the cost of a 30-second advertisement for Super Bowl 40.

• $3

• $15

• $58,153

• $83,132

• $2,824,947

Tags

CCSS.HSF-LE.A.1B

A scatterplot of y versus x shows a positive, nonlinear association. Two different transformations are attempted to try to linearize the association: using the logarithm of the y values and using the square root of the y values. Two least-squares regression lines are calculated, one that uses x to predict log(y) and the other that uses x to predict the square root of y. Which of the following would be the best reason to prefer the least-squares regression line that uses x to predict log(y)?

• The value of r² is smaller.

• The standard deviation of the residuals is smaller.

• The slope is greater.

• The residual plot has more random scatter.

• The distribution of residuals is more Nomal.