ACT 1 Alg: Identify an approximate line of best fit

Welcome to your ACT 1 Alg: Identify an approximate line of best fit

$Q_{1}:$ ............... is a mathematical diagram represented by a set of dots that display the relationship between two numerical variables.

A scatter plot

A positive association

A regression line

A fit line

$Q_{2}:$ If the slope of a regression line is negative, then the two variables have.............?

a positive association

a negative association

no association

none

$Q_{3}:$ Which of the following is true?

Regression line cannot be determined

Regression line with negative slope

regression line with positive slope

none

$Q_{4}:$ Which of the following is true?

Regression line cannot be determined

Regression line with negative slope

regression line with positive slope

none

$Q_{5}:$ The scatter plot below shows the average scores of $10$ golfers and their weekly practice times. The line of best fit is also shown. What is the average score of the golfer that is farthest from the line of best fit?

$99$

$98$

$96$

$93$

$Q_{6}:$ The scatter plot below shows the average scores of $10$ golfers and their weekly practice times. The line of best fit is also shown. There are two golfers whose average practice time is the same. What is the difference between their average scores?

$10$

$6$

$8$

$4$

$Q_{7}:$ What is the median score of the $105, 104, 100, 99, 98, 96, 93, 90, 88, 86$ golfers?

$96$

$97$

$98$

$99$

$Q_{8}:$ According to the line of best fit in the scatter plot below, which of the following best approximate the year in which the number of cars repaired by Jay’s Motor was estimated to be $4500$?

$1996$

$1998$

$2000$

$2002$

$Q_{9}:$ One of the following sentences is false?

Some scatter plots are not linear.

A scatter plot with a quadratic model that as $x$ increases, $y$ falls then rises, only.

The best fit line is regression line.

The $x$-coordinate of the dot, measured along the horizontal axis, gives the value of one variable.

$Q_{10}:$ The scatter plot at the below shows the prices and weights of various boxed products. Of the five labeled products, which has the best unit price?

$A$

$B$

$C$

$D$

$Q_{11}:$ Which of the following is represent the graph below ?

A scatter plot with a quadratic model shows that as $x$ increases, $y$ falls then rises.

A scatter plot with a quadratic model shows that as $x$ increases, $y$ rises then falls.

A scatter plot with an exponential model shows a positive association that is not linear.

A scatter plot with an exponential model shows a negative association that is not linear.

$Q_{12}:$ The graph below is a scatter plot with $8$ points, each representing the low temperature and high temperature of 8 days in September in a certain city. Both the low temperatures and high temperatures are measured in degrees Fahrenheit. The line of best fit for the data is also shown. Based on the line of best fit for the data shown, how many degrees does the high temperature increase when the low temperature increases by one degree?

$0.9$

$1.3$

$1.6$

$1.8$

$Q_{13}:$ The graph below is a scatter plot with $8$ points, each representing the low temperature and high temperature of 8 days in September in a certain city. Both the low temperatures and high temperatures are measured in degrees Fahrenheit. The line of best fit for the data is also shown. What is the predicted high temperature of the day when the low temperature is $58$?

$65$

$68$

$71$

$74$

$Q_{14}:$ The graph below is a scatter plot with $8$ points, each representing the low temperature and high temperature of 8 days in September in a certain city. Both the low temperatures and high temperatures are measured in degrees Fahrenheit. The line of best fit for the data is also shown. Among the four days marked $1, 2, 3,$ and $4$ in the scatter plot, on which day is the difference between the high temperature and the low temperature minimal?

Day $1$

Day $2$

Day $3$

Day $4$

$Q_{15}:$ Which of the following is an equation in slope-intercept form for the line that is drawn ?

$ y = 0.415x - 0.735$

$ y = \frac{17}{41}x - \frac{3}{41}$

$ y = \frac{-17}{41}x - \frac{3}{41}$

$ y = \frac{17}{41}x + \frac{3}{41}$

$Q_{16}:$ You have a scatterplot of data points and want to find an approximate line of best fit. What type of line should you draw through the data points to best represent the trend?

A vertical line

A horizontal line

A diagonal line

A straight line that minimizes the sum of the squared vertical distances from the data points to the line.

$Q_{17}:$ You are given a set of data points representing the relationship between the number of hours studied and the test scores of students. What type of line should you use as the best-fit line to make predictions about a student's test score based on their study hours? A) A curved line B) A wavy line C) A straight line D) A zigzag line

A curved line

A wavy line

A straight line

A zigzag line

$Q_{18}:$ In a scatterplot, the data points appear to follow a straight-line pattern that slopes upward from left to right. What can you conclude about the relationship between the two variables?

There is a negative correlation.

There is no correlation.

There is a positive correlation.

There is a quadratic relationship.

$Q_{19}:$ You have data on the ages and heights of a group of children. You want to use a line of best fit to predict the height of a child based on their age. What type of relationship are you trying to model?

Linear

Exponential

Quadratic

No relationship exists.

$Q_{20}:$ You have plotted data points on a graph and drawn a line of best fit. If a new data point falls significantly above the line, what can you infer?

The data point is an outlier.

The line of best fit is incorrect.

The data point is irrelevant.

The data point confirms the trend.

$Q_{21}:$ In a scatterplot, you notice that the data points are widely dispersed and do not follow a clear linear trend. What type of line of best fit is most appropriate in this case?

A straight line

A curved line

No line of best fit

A vertical line

$Q_{22}:$ You have plotted data points on a graph and drawn a line of best fit. The equation of the line is $ y=2x+3$. What does the coefficient of $x (2)$ represent in this equation?

The slope of the line

The $y$-intercept of the line

The correlation coefficient

The error in the line

$Q_{23}:$ You have data on the number of ice creams sold and the temperature on a particular day. The line of best fit through the data points has a negative slope. What can you conclude about the relationship between temperature and ice cream sales?

As temperature increases, ice cream sales increase.

There is no relationship between temperature and ice cream sales.

As temperature increases, ice cream sales decrease.

The relationship is nonlinear.

$Q_{24}:$ In a scatterplot, the data points are closely grouped around a straight-line pattern. What can you infer about the strength of the linear relationship?

The relationship is weak.

The relationship is strong.

There is no linear relationship.

The data points are outliers.

$Q_{25}:$ You have data on the number of hours spent practicing a musical instrument and the level of proficiency achieved. You plot the data points and draw a line of best fit. What type of line would be most appropriate in this case to predict proficiency based on practice hours?

A straight line

A sinusoidal line

A zigzag line

A vertical line

Name