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In this lesson, we will learn how to find and use the least squares regression line equation.

Q1:

The scatterplot shows a set of data for which a linear regression model appears appropriate.

The data used to produce this scatterplot is given in the table shown.

Calculate the equation of the least squares regression line of π¦ on π₯ , rounding the regression coefficients to the nearest thousandth.

Q2:

The table shows the price of a barrel of oil and the economic growth. Using the information in the table, estimate the economic growth if the price of a barrel of oil is 35.40 dollars.

Q3:

Given that points ( 3 , β 9 ) and ( 2 , β 4 ) lie on a regression line π¦ on π₯ , which of the following points does not lie on the same line?

Q4:

Two variables π and π have a correlation coefficient of π and their mean and standard deviations are denoted by π , π , π π , and π π , respectively. Which of the following is the formula for calculating the slope, π , of the least squares regression line π = π + π π ?

Q5:

Using the information in the table, find the regression line Μ π¦ = π + π π₯ . Round π and π to 3 decimal places.

Q6:

Q7:

Given the quadratic regression model π¦ = 3 π₯ β 5 π₯ + 2 2 , calculate the value of π¦ when π₯ is equal to 2.7.

Q8:

The following table shows the relation between the lifespan of cars in years and their selling price in thousands of pounds. Find the equation of the line of regression in the form Μ π¦ = π + π π₯ , writing π and π to 3 decimal places.

Q9:

For a given data set, ο π₯ = 4 7 , ο π¦ = 4 5 . 7 5 , ο π₯ = 3 2 9 ο¨ , ο π¦ = 3 8 9 . 3 1 2 5 ο¨ , ο π₯ π¦ = 3 1 0 . 2 5 , and π = 8 . Calculate the value of the regression coefficient π in the least squares regression model π¦ = π + π π₯ . Give your answer correct to three decimal places.

Q10:

The latitude ( π₯ ) and the average temperatures in February ( π¦ , measured in β C ) of 10 world cities were measured. The calculated least squares linear regression model for this data was π¦ = 3 5 . 7 β 0 . 7 1 3 π₯ .

What is the interpretation of the value of β 0 . 7 1 3 in the model?

What is the interpretation of the value of 35.7 in the model?

Q11:

Using the information in the table, estimate the value of π¦ when π₯ = 1 3 . Give your answer to the nearest integer.

Q12:

Using the information in the table, find the error in π¦ if π₯ = 2 2 . Give your answer to the nearest integer.

Q13:

An ice cream salesman records data on the number of ice creams sold each day and the temperature at midday during the April-November period. He fits a linear regression model of the form π¦ = π + π π₯ to the data. Would you expect the regression coefficient π to be positive or negative in this context?

Q14:

The table shows the price of a barrel of oil and the economic growth. Using the information in the table, find the regression line Μ π¦ = π + π π₯ . Round π and π to 3 decimal places.

Q15:

Q16:

Q17:

Q18:

Given the quadratic regression model π¦ = β π₯ + 5 . 2 π₯ β 2 . 1 2 , calculate the value of π¦ when π₯ is equal to 3.

Q19:

A city council is investing in improving their bus services. Over a five-year period, they collect data on the amount of money invested in each bus route ( π₯ , measured in 100s of dollars) and the percent of bus services that run on time ( π¦ , measured in %). They find that the data can be described by the linear regression model π¦ = 5 2 . 3 + 2 . 7 π₯ .

What is the interpretation of the value of 2.7 in the regression model?

What is the interpretation of the value of 52.3 in the regression model?

Q20:

The relationship between the distances jumped by competitors in the long jump and high jump during the womenβs heptathlon at the 2016 Rio Olympics can be modeled by the regression line .

What is the interpretation of the value 0.218 in the regression model?

What is the interpretation of the value 0.483 in the regression model?

Does the interpretation of the value 0.483 seem reasonable in the context of the data?

Estimate, to the nearest hundredth of a meter, the expected high jump result for a competitor who jumped 6.03 m in the long jump competition.

Q21:

The scatterplot shows the high jump and long jump results achieved by 15 competitors in the womenβs heptathlon competition in the 2016 Rio Olympics.

Does a linear model appear to be appropriate for modeling this data set?

Would you expect the regression coefficient of this model to be positive or negative?

The data table shows the numerical data used to produce the scatter diagram.

Representing long jump by π₯ and high jump by π¦ , find the values of π , π π₯ π₯ π¦ π¦ , and π π₯ π¦ to the nearest thousandth.

Hence, calculate the equation of the regression line of π¦ on π₯ .

Q22:

Amir conducted a statistical experiment to measure the number of goals as a function of the number of soccer games. With the number of soccer games as his independent variable and the number of goals as his dependent variable, the line of best fit had a slope of 2.28. What does this mean?

Q23:

A linear model was fitted to three data sets. The residual plot for each data set is shown. For which data set is a linear model appropriate?

Q24:

The table shows the relation between the variables π₯ and π¦ . Find the equation of the regression line in the form Μ π¦ = π + π π₯ . Approximate π and π to 3 decimal places.

Q25:

Given the regression line Μ π¦ = 7 . 3 π₯ β 5 . 9 , find the expected value of π¦ when π₯ = 3 0 .

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