Interpreting Values
Predicted Values and Residuals
LSRL
Describing
Review
100
A new process designed to increase the temperature inside steel girders shows great promise. Using an initial temperature (degree C), we can predict the final temperature (degree C) by using a slope of 1.095. Interpret that value.
For each additional degree in initial temperature there is a 1.095 degree predicted increase in final temperature.
100
A scatterplot displays the association between the size of a diamond (in carats) and its retail price (in Singapore dollars) for 48 observations. Use the model to predict the cost of a 0.25 carat diamond.
cost-hat=197+ 4,000(size)
1,197 Singapore Dollars
100
A bivariate set of data relates the amount of annual salary raise and previous performance rating. The least-squares regression equation
y-hat = 1,400 + 2,000x ,
where ^ y is the estimated raise and x is the performance rating. Identify the slope value and y-intercept value.
slope: 2,000
y-int: 1,400
100
This graph shows the relationship between two quantitative variables.
What is a scatterplot?
100
What is wrong with the following statement?
The correlation between baseball position and number of hits at bat is .93.
Correlation only measures quantitative variables.
200
A new process designed to increase the temperature inside steel girders shows great promise. Using an initial temperature (degree C), we can predict the final temperature (degree C). The equation has a y-intercept of 37. Interpret the value.
There's a predicted final temperature of 37 degrees C, when the initial temperature is 0 degrees C.
200
Using the model:
cost-hat=197+ 4,000(size)
Calculate the residual for a diamond with 0.31 carats and a cost of 1,500 Singapore Dollars
1500-1437= 63
200
Explain why it isn’t correct to say that the correlation is 0.87 mg/cal.
correlation has no units of measure
200
These are the four features that you describe when describing a scatterplot.
What is direction, form, strength, and outliers?
200
The linear relationship between number of dentist visits and number of cavities is #of cavities=-1.3 (# of office visites +6, the coefficient of determination is 74.3%. Correlation is ?
What is -.86
300
What does r= -.73 tell you about the correlation?
There's a strong, negative linear association between variables
300
Use the residual plot to answer whether a linear model is appropriate in this case.
A strong pattern indicates a linear model is NOT appropriate
300
If the average time to complete a task is 27.7 seconds, with a standard deviation of 9.3 and the average age in years of participants is 34.1 with a standard deviation of 5.4, find the slope for the LSRL that would model using age to predict the time it would take to complete the task. Given r = - 0.83
b1= -0.482
300
This variable goes on the x-axis and this variable goes on the y-axis.
What is the explanatory on the x-axis and the response on the y-axis?
300
These are the four feature you describe when describing a distribution.
What is center, shape, spread, and outliers?
400
98% of the variation in weight gain can be explained by the variation in calories consumed. Name this value, and find correlation.
r-squared or coefficient of determination
r= -0.99
400
What is it called when you make a prediction using your model for an x-value outside your data set?
Extrapolation
400
What point does EVERY LSRL model go through?
( x-bar, y-bar)
400
You would look at this plot to check to see whether a linear regression is appropriate.
What is the residual plot?
400
Using N(1152, 84), the Normal model for weights of Angus steers, this percent of steers weigh over 1250 pounds.
What is 12%?
500
What does a positive residual indicate?
The linear model has made an under prediction or the actual value is larger than the predicted value.
500
The smallest tree has an actual height of 312 cm. Find its predicted value, without the model.
-40=312-p
p=352 cm
500
The proper name for the line-of-best-fit is the "Least Squares Regression Line"... What goal does this line achieve that gives it its name?
It minimizes the sum of the squared residuals
ie, minimized the sum of the squares from the response variable to the predicted response variable.
500
The percent of variability in the response variable that is explained by the linear relationship given the explanatory variable.
What is r squared or coefficient of determination?
500
Given the following 5 number summary, state the shape of the distribution: 1, 10, 15, 16, 17
What is skewed to the left?