In simple linear regression analysis, the least squares
regression line minimizes the sum of the squared differences
between actual and predicted y values.
True
False
Question 1: If R squared=0.64 for the linear
regression equation Y= 3.2X+ 2.8 + error , Where Y (or response
variable) = stopping distance and X (or explanatory variable)=
Velocity which of the following are true?
a.) That 64 % of the variation in Stopping distance is
explained by velocity and the correlation coefficient R= -0.8
b.) That 64 % of the variation in Stopping distance is
explained by velocity and the correlation coefficient R= 0.8
c.) That velocity (X)...
1. Obtain a linear regression equation for the data to predict
the mean temperature values for any given CO2 level. How good is
the linear fit for this data? Explain using residual plot and
R-square value. To draw residual plot, compute the estimated
temperatures for every value of the CO2 level using the regression
equation. Then compute the difference between observed (y) and
estimated temperature values (called residual; ). Plot the
residuals versus CO2 level (called a residual plot).
320.09...
Find the equation of the least-squares regression line ŷ and the
linear correlation coefficient r for the given data. Round the
constants, a, b, and r, to the nearest hundredth.
{(0, 10.8), (3, 11.3), (5, 11.2), (−4, 10.7), (1, 9.3)}
Linear Regression
Linear regression is used to predict the value of one variable
from another variable. Since it is based on correlation, it cannot
provide causation. In addition, the strength of the relationship
between the two variables affects the ability to predict one
variable from the other variable; that is, the stronger the
relationship between the two variables, the better the ability to
do prediction.
What is one instance where you think linear regression
would be useful to you in...
Curve Fitting and Linear Regression
a) Determine the linear regression equation
for the measured values in the table above.
??
1
2
3
4
Value 1 (????)
0
3
7
10
Value 2 (????)
2
4
9
11
b) Plot the points and the linear
regression curve.
c) Determine the Linear Correlation
Coefficient (i.e., Pearson’s r) for the dataset in the
table above.
Run a linear regression using Excel’s Data Analysis regression
tool. Construct the linear regression equation and determine the
predicted total sales value if the number of promotions is 6. Is
there a significant relationship? Clearly explain your reasoning
using the regression results.
Number of Promotions
Total Sales
3
2554
2
1746
11
2755
14
1935
15
2461
4
2727
5
2231
14
2791
12
2557
4
1897
2
2022
7
2673
11
2947
11
1573
14
2980
Linear Regression
When we use a least-squares line to predict y values for x
values beyond the range of x values found in the data, are we
extrapolating or interpolating? Are there any concerns about such
predictions?