Acrylamide is a chemical that is sometimes found in cooked starchy foods and which is thought to increase the risk of certain kinds of cancer. The paper "A Statistical Regression Model for the Estimation of Acrylamide Concentrations in French Fries for Excess Lifetime Cancer Risk Assessment"† describes a study to investigate the effect of x = frying time (in seconds) and y = acrylamide concentration (in micrograms per kg) in French fries. The data in the accompanying table are approximate values read from a graph that appeared in the paper. FryingTime AcrylamideConcentration 150 155 240 115 240 190 270 180 300 140 300 265 (a) Construct a scatterplot of these data. A scatterplot has 6 points.The horizontal axis is labeled "x" and ranges from 100 to 350.The vertical axis is labeled "y" and ranges from 50 to 350.The points are plotted from left to right in a horizontal direction starting from the lower left side of the diagram.Along the horizontal axis, there is 1 point at 150, 2 points at 240, 1 point at 270, and 2 points at 300.The points are scattered and are between the approximate horizontal axis values of 150 and 300 and between the approximate vertical values of 100 and 230. A scatterplot has 6 points.The horizontal axis is labeled "x" and ranges from 100 to 350.The vertical axis is labeled "y" and ranges from 50 to 350.The points are plotted from left to right in an upward, diagonal direction starting from the lower left of the diagram.Along the horizontal axis, there is 1 point at 150, 2 points at 240, 1 point at 270, and 2 points at 300.The points are scattered and are between the approximate horizontal axis values of 150 and 300 and between the approximate vertical values of 110 and 270. A scatterplot has 6 points.The horizontal axis is labeled "x" and ranges from 100 to 350.The vertical axis is labeled "y" and ranges from 50 to 350.The points are plotted from left to right in an upward, diagonal direction starting from the lower left of the diagram.Along the horizontal axis, there is 1 point at 150, 2 points at 240, 1 point at 270, and 2 points at 300.The points are somewhat scattered and are between the approximate horizontal axis values of 150 and 300 and between the approximate vertical values of 140 and 220. A scatterplot has 6 points.The horizontal axis is labeled "x" and ranges from 100 to 350.The vertical axis is labeled "y" and ranges from 50 to 350.The points are plotted from left to right in a downward, diagonal direction starting from the upper left of the diagram.Along the horizontal axis, there are 2 points at 150, 1 point at 180, 2 points at 210, and 1 point at 300.The points are scattered and are between the approximate horizontal axis values of 150 and 300 and between the approximate vertical values of 110 and 270. (b) Find the equation of the least-squares line. (Round your answers to three decimal places.) ŷ = + xBased on this line, what would you predict acrylamide concentration (in micrograms per kg) to be for a frying time of 240 seconds? What is the residual (in micrograms per kg) associated with the observation (240, 190)? (Round your answers to two decimal places.) predicted value micrograms per kgresidual micrograms per kg
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Acrylamide is a chemical that is sometimes found in cooked starchy foods and which is thought to increase the risk of certain kinds of cancer. The paper "A Statistical Regression Model for the Estimation of Acrylamide Concentrations in French Fries for Excess Lifetime Cancer Risk Assessment"† describes a study to investigate the effect of x = frying time (in seconds) and y = acrylamide concentration (in micrograms per kg) in French fries. The data in the accompanying table are approximate values read from a graph that appeared in the paper.
Frying
Time
Acrylamide
Concentration
150
155
240
115
240
190
270
180
300
140
300
265
(a)
Construct a
A scatterplot has 6 points.
The horizontal axis is labeled "x" and
The vertical axis is labeled "y" and ranges from 50 to 350.
The points are plotted from left to right in a horizontal direction starting from the lower left side of the diagram.
Along the horizontal axis, there is 1 point at 150, 2 points at 240, 1 point at 270, and 2 points at 300.
The points are scattered and are between the approximate horizontal axis values of 150 and 300 and between the approximate vertical values of 100 and 230.
A scatterplot has 6 points.
The horizontal axis is labeled "x" and ranges from 100 to 350.
The vertical axis is labeled "y" and ranges from 50 to 350.
The points are plotted from left to right in an upward, diagonal direction starting from the lower left of the diagram.
Along the horizontal axis, there is 1 point at 150, 2 points at 240, 1 point at 270, and 2 points at 300.
The points are scattered and are between the approximate horizontal axis values of 150 and 300 and between the approximate vertical values of 110 and 270.
A scatterplot has 6 points.
The horizontal axis is labeled "x" and ranges from 100 to 350.
The vertical axis is labeled "y" and ranges from 50 to 350.
The points are plotted from left to right in an upward, diagonal direction starting from the lower left of the diagram.
Along the horizontal axis, there is 1 point at 150, 2 points at 240, 1 point at 270, and 2 points at 300.
The points are somewhat scattered and are between the approximate horizontal axis values of 150 and 300 and between the approximate vertical values of 140 and 220.
A scatterplot has 6 points.
The horizontal axis is labeled "x" and ranges from 100 to 350.
The vertical axis is labeled "y" and ranges from 50 to 350.
The points are plotted from left to right in a downward, diagonal direction starting from the upper left of the diagram.
Along the horizontal axis, there are 2 points at 150, 1 point at 180, 2 points at 210, and 1 point at 300.
The points are scattered and are between the approximate horizontal axis values of 150 and 300 and between the approximate vertical values of 110 and 270.
(b)
Find the equation of the least-squares line. (Round your answers to three decimal places.)
ŷ = +
x
Based on this line, what would you predict acrylamide concentration (in micrograms per kg) to be for a frying time of 240 seconds? What is the residual (in micrograms per kg) associated with the observation (240, 190)? (Round your answers to two decimal places.)
predicted value
micrograms per kg
residual
micrograms per kg
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