Exam 7: Linear Regression

A regression analysis of students' college grade point averages (GPAs) and their high school GPAs found $R ^ { 2 } = 0.311$ . Which of these is true? I. High school GPA accounts for $31.1 \%$ of college GPA. II. $31.1 \%$ of college GPAs can be correctly predicted with this model. III. $31.1 \%$ of the variance in college GPA can be accounted for by the model

A company studying the productivity of its employees on a new information system was interested in determining if the age $( X )$ of data entry operators influenced the number of completed entries made per hour (Y). The regression equation is $\hat { y } = 14.374 - 0.145 x$ . Suppose the actual completed entries per hour for an operator who is 35 years old was 8 . The residual is

A company studying the productivity of their employees on a new information system was interested in determining if the age $( X )$ of data entry operators influenced the number of completed entries made per hour (Y). The regression equation is $\hat { y } = 14.374 - 0.145 x$ . If $s _ { x } = 14.04$ and $s _ { y } = 2.61$ , then the correlation coefficient between age and productivity is

A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each Variety of coffee were sold last month. PRICE PER POUND POUNDS SOLD \ 3.99 75 \ 5.99 60 \ 7.00 65 \ 12.00 45 \ 4.50 80 \ 7.50 70 \ 15.00 25 \ 10.00 35 \ 12.50 40 Mean \ 8.99 50 Standard Deviation \ 3.63 54.50 18.33 Based on the data and summary statistics shown below, the slope of the estimated regression Line that relates the response variable (monthly sales) to the predictor variable (price per Pound) is

A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each Variety of coffee were sold last month. PRICE PER POUND POUNDS SOLD \ 3.99 75 \ 5.99 60 \ 7.00 65 \ 12.00 45 \ 4.50 80 \ 7.50 70 \ 15.00 25 \ 10.00 35 \ 12.50 40 \ 8.99 50 Mean Ctandard \ 8.75 54.50 Deviation 18.33 Based on the data and summary statistics, the intercept of the estimated regression line that Relates the response variable (monthly sales) to the predictor variable (price per pound) is

A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each Variety of coffee were sold last month. PRICE PER POUND POUNDS SOLD Mean \ 8.75 54.50 Standard Deviation \ 3.63 18.33 Correlation - Based on the summary statistics shown below, what percent of the variability in the number Of pounds of coffee sold per week can be explained by price?

If the point in the upper left corner of the scatterplot is removed, what will happen to the correlation (r) and the slope of the line of best fit (b)?

R-sq is a measure of ...

The correlation coefficient between high school grade point average (GPA) and college GPA is 0.560.For a student with a high school GPA that is 2.5 standard deviations above the Mean, we would expect that student to have a college GPA that is ______ the mean.

Residuals are …

It' s easy to measure the circumference of a tree' s trunk, but not so easy to measure its height. Foresters developed a model for ponderosa pines that they use to predict the tree' $s$ height (in feet) from the circumference of its trunk (in inches): $\ln \hat { h } = - 1.2 + 1.4 ( \ln C$ ). A lumberjack finds a tree with a circumference of $60 ^ { \prime \prime }$ ; how tall does this model estimate the tree to be?

Data were collected on monthly sales revenues (in $\$ 1,000 \mathrm {~s}$ ) and monthly advertising expenditures $( \$ 100$ s) for a sample of drug stores. The regression line relating revenues (Y) to advertising expenditure $( \mathrm { X } )$ is estimated to be $\hat { y } = - 48.3 + 9.00 x$ . The predicted sales revenue for a month in which $\$ 1,000$ was spent on advertising is

Suppose the correlation, r, between two variables x and y is -0.44.What percentage of the variability in y cannot be explained by x?

Suppose the correlation, r, between two variables x and y is -0.44.What would you predict about a y value if the x value is 2 standard deviations above its mean?

Data were collected on monthly sales revenues (in $\$ 1,000 \mathrm {~s}$ ) and monthly advertising expenditures $( \$ 100 \mathrm {~s} )$ for a sample of drug stores. The regression line relating revenues $( \mathrm { Y } )$ to advertising expenditure $( X )$ is estimated to be $\hat { y } = - 48.3 + 9.00 x$ . The correct interpretation of the slope is that for each additional

An 8th grade class develops a linear model that predicts the number of cheerios (a small round cereal) that fit on the circumference of a plate by using the diameter in inches.Their Model is cheerios = 0.56 + 5.11(diameter). If the diameter is increased from 4 inches to 14 inches, the predicted number of cheerios will Increase by about…

An 8th grade class develops a linear model that predicts the number of cheerios (a small round cereal) that fit on the circumference of a plate by using the diameter in inches.Their Model is cheerios = 0.56 + 5.11(diameter). The slope of this model is best interpreted in context as…

If the point in the upper right corner of this scatterplot is removed from the data set, then what will happen to the slope of the line of best fit (b) and to the correlation (r)?