Question

has collected the following data from a certain sample.

x	2	3	4	5	6	7	8
y	3	4	3	5	7	7	8

complete the parts below to help denise find a relationship between x and y for the dataset.
(a) to see if there are any trends in the data, denise wants to create a scatter plot. she plotted the first four data points. plot the remaining three data points.
(b) the data seems to have a linear trend. so, denise wants to find a linear equation that could approximately model the data. select \compute\ to generate the values used for a linear regression model. write the values in your answer to 3 decimal places.

x	2	3	4	5	6	7	8
y	3	4	3	5	7	7	8

line reg: $y = ax + b$
$a \approx 0.7395$
$b \approx 1.137$
$r^2 \approx 0.887$
$r \approx 0.942$
the linear equation that best fits the data is $y = \square$
(c) use the equation from part (b) to help denise predict the value of y when $x = 1$. write your answer to 3 decimal places.
$y \approx \square$

Explanation:

Step1: Identify the linear equation form

The linear equation is given by \( y = ax + b \), where \( a = 0.7395 \) and \( b = 1.537 \). We need to round these values to 3 decimal places.

• Rounding \( a = 0.7395 \) to 3 decimal places: The fourth decimal is 5, so we round up the third decimal. Thus, \( a \approx 0.740 \).
• Rounding \( b = 1.537 \) to 3 decimal places: It already has three decimal places, so \( b = 1.537 \).

Step2: Write the linear equation

Substitute the rounded values of \( a \) and \( b \) into the equation \( y = ax + b \). So the equation becomes \( y = 0.740x + 1.537 \).

Step3: Predict y when x = 1

Substitute \( x = 1 \) into the equation \( y = 0.740x + 1.537 \).

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Answer:

• Part (b) linear equation: \( y = 0.740x + 1.537 \)
• Part (c) predicted y when x = 1: \( 2.277 \)