Question

In the least squares = ,

a) what is the value of the slope?

b) When increases 1 unit, by how much does change?

Answer #1

Let x be independent variable and y be dependent variable.

Least square Regression equation is

= a + b *x

where a is intercept and b is slope and is predicted value of y for some x.

**The slope is rate of change when x increases by 1 unit
then the
changes by b units.If slope is positive then the
increases and if slope is negative then
decreases.**

or

The slope of the least squares regression line is given by
where r is the correlation coefficient,
sx is the standard deviation of the
X‑values, and sy is the standard
deviation of the Y‑values. If r = 0.25,
sx = 2, and
sy = 5, then how much should we expect
Y to decrease for every one unit of increase in X?

Find the slope from the least-squares regression line for the
data below of final grade as a percent and days absent. What does
it tell us about the relationship?
Final Absences
81 1
90 0
86 2
76 3
51 6
75 4
44 7
81 2
94 0
93 1
A. Slope is 94.695 For each day absent the student's final grade
increase by 0.947%
B. Slope is -94.695. For each day absent the student's final
grade decrease by...

Select all the statements that are true of a least-squares
regression line.
1. R2 measures how much of the variation in Y is explained by X
in the estimated linear regression.
2.The regression line maximizes the residuals between the
observed values and the predicted values.
3.The slope of the regression line is resistant to outliers.
4.The sum of the squares of the residuals is the smallest sum
possible.
5.In the equation of the least-squares regression line, Y^ is a
predicted...

Carrie and Ryan have both computed the slope of the
least-squares line using data for which the standard deviation of
the x-values and the standard deviation of the y-values are equal.
Carrie gets a value of 0.5 for the slope, and Ryan gets a value of
2. One of them is right. Which one?

Compute the least-squares regression equation for the
given data set. Round the slope and
y
-intercept to at least four decimal places.
x
6
1
4
7
3
y
2
4
1
7
6
Regression line equation: y=?

compute the least-squares regression equation for the
given data set. Round the slope and
y
-intercept to at least four decimal places.
x
7
4
5
2
1
y
2
6
5
1
7
Regression line equation: y=

Compute the least-squares regression equation for the given data
set. Round the slope and y -intercept to at least four decimal
places. x 5 4 2 6 3 y 4 5 1 3 6 Send data to Excel Regression line
equation: = y

The least squares method will minimize the sum of squares
_______ when describing the equation that best fits the ordered
pairs.

The length of a snake is related to its age. The EQUATION for
the Least Squares Regression Line is the following
MEAN LENGTH = 15 + 10*YEARS
About how long would a snake be when it is 20 years old?
A. Close to 120
cm
B. Close to 25
cm
C. Close to 400
cm
D. Close to 220
cm
E. NOT
ENOUGH INFORMATION
Which of the following is closest to the correlation of age and
length, if the R squared value of the estimated...

Find the slope of the equation of the least-squares regression
line for the following data set.
x
y
59
-119
24
-35
50
-107
47
-73
41
-78
72
-117
40
-55
Round your answer to two decimal places.

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