APS: Unit 2- Linear Regression

The scatterplot above shows the batting average and the number of home runs by each player on a summer baseball team. Which of the following best describes the plot?

• possibly linear, very scattered

• positive, linear, somewhat scattered

• negative, linear, somewhat scattered

• nonlinear, quadratic, somewhat scattered

• nonlinear, exponential, very scattered

A scatterplot shows a linear association, and a residual plot for the linear regression shows no pattern. The regression yielded the information shown above. Which of the following is false?

• The LSRL is a good linear model for this data.

• The high R value means that it is reasonable to assume a cause-and-effect relationship between the two variables.

• Because a new LSRL after removal of one of the points is

  ŷ = 16.72 + 2.51x, the point that was removed can be considered an influential point.

• For every unit increase in x, the predicted y-value will increase by approximately 2.701 units.

• The association is strong and positive.

Twenty types of beef hot dogs were tested for calories and sodium (mg). The hot dogs averaged 156.85 calories with a standard deviation of 22.64, and the sodium level averaged 401.15 mg with a standard deviation of 102.43 mg. The correlation was given as r = 0.887. The equation of the LSRL predicting sodium level from number of calories is:

• ŷ = -228.30 + 4.01x

• ŷ = 22.64 - 156.85x

• ŷ = 102.43 - 401.15x

• ŷ = 4.01 - 228.33x

• ŷ = 78.19 + 0.196x

Tags

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8

Data that follow an exponential model in (x, y) can be re-expressed as a linear model if you plot:

• (log x, y)

• (x, log y)

• (log x, log y)

• (x, y²)

• (x, √y)

Use the scatterplot and computer printout shown above to answer the following question.

The correlation and coefficient of determination are:

• -0.94 and 0.97

• -0.94 and 0.89

• -0.93 and 0.94

• 0.89 and 0.94

• 0.94 and -0.89

Use the scatterplot and computer printout shown above to answer the following question.

Write the equation of the least squares regression line.

• ŷ = -.050 + 0.07x

• ŷ = -0.50 - 0.866x

• ŷ = 8.66 - 0.50x

• ŷ = 8.66 + 0.69x

• ŷ = 12.55 - 6.81x

Use the scatterplot and computer printout shown above to answer the following question.

Because of inflation, the cost per unit increases by 25 cents. The correlation for the revised data will be:

• 0.25 x original correlation.

• 0.25 + original correlation.

• 25 x original correlation.

• 25 + original correlation.

• original correlation.

Use the scatterplot and computer printout shown above to answer the following question.

Which of the following is a correct interpretation of the coefficient of determination?

• Approximately 89% of the data are explained by the least squares regression line.

• Approximately 89% of the least squares regression line is explained by the data.

• Approximately 89% of the variation in the cost can be explained by its linear relationship with number of units purchased.

• Approximately 89% of the variation in the number of units purchased can be explained by its linear relationship with the cost.

• None of these is a correct interpretation.

Use the scatterplot and computer printout shown above to answer the following question.

The residual for 8 units purchased is -0.8074. This tells us that our predicted cost is:

• higher than our observed cost.

• lower than our observed cost.

• wrong.

• the result of extratpolation.

• the result of interpolation.

If the data point in the lower right-hand corner of the graph is removed, which of these will be the result?

• The slope of the least squares regression line will decrease and the correlation will increase.

• The slope of the least squares regression line will increase and the correlation will increase.

• The slope of the least squares regression line will decrease and the correlation will decrease.

• The slope of the least squares regression line will increase and the correlation will decrease.

• The slope of the least squares regression line and the correlation will remain the same.

Tags

CCSS.HSS.ID.A.3

CCSS.HSS.ID.B.6

CCSS.HSS.ID.C.7

CCSS.HSS.ID.C.8