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Chapter 3: Q.43 (page 191)

Least-squares idea The table below gives a small set of data. Which of the following two lines 铿乼s the data better: y^=1鈭�xory^=3鈭�2x? Make a graph of the data and use it to help justify your answer. (Note: Neither of these two lines is the least-squares regression line for these data.)

Short Answer

Expert verified

The lineY鈭�=3-2fits the data better.

Step by step solution

01

Given Information

It is given in the question that,y^=1鈭�xory^=3鈭�2x

02

Explanation

Below is the scatter plot for the data given,

By using a red line, the line Y鈭�=1-Xcan be seen and by using a green line, it can be seen that Y鈭�=3-2Xcan be seen.

The figure shows that lineY鈭�=1-Xfits better in a scatter plot since it passes through only two points and that the rest of the points follow this line closely.

The data is, therefore, better suited toY鈭�=3-2X.

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Most popular questions from this chapter

Beer and blood alcohol The example on page 182describes a study in which adults drank different amounts of beer. The response variable was their blood alcohol content (BAC). BAC for the same amount of beer might depend on other facts about the subjects. Name two other variables that could account for the fact that r2=0.80.

A recent study discovered the correlation between the age at which an infant first speaks and the child鈥檚 score on an IQ test given upon entering elementary school is 鈭�0.68. A scatterplot of the data shows a linear form. Which of the following statements about this finding is correct?

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(d) There is a moderately strong, negative linear relationship between age at first spoken word and later IQ test scores for the individuals in this study.

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(a) Identify the slope of the line and explain what it means in this setting.

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