In simple linear regression analysis, the least squares
regression line minimizes the sum of the squared...
In simple linear regression analysis, the least squares
regression line minimizes the sum of the squared differences
between actual and predicted y values.
The regression line minimizes the sum of the squared errors
True o false
F significance is used to determine how fit is the model
True o false
The best model is a statistically significant model with a high
r-square and few variables
True o false
The exponential smoothing with trend model uses two smoothing
constants, one constant works as in the exponential smoothing model
and the other adjusts the line for presence of a trend
True o false
An exponential...
What are Least Squares Assumptions for simple linear regression?
For each least
squares assumption, provide an example in which the assumption is
valid, then provide
an example in which the assumption fails.
A simple linear least squares regression of the heights (in
feet) of a building on the number of stories in the building was
performed using a random sample of 30 buildings. The associated
ANOVA F statistic was 5.60. What is the P-value
associated with this ANOVA F test?
a.) greater than 0.10
b.) between 0.001 and 0.01
c.) between 0.01 and 0.025
d.) between 0.05 and 0.10
e.) between 0.025 and 0.05
f.) less than 0.001
Prove that the least squares estimates in a simple linear
regression model are unbiased. Be sure to state carefully the
assumptions under which your proof holds.
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)}
A least-squares simple linear regression model was fit
predicting duration (in minutes) of a dive from depth of the dive
(in meters) from a sample of 45 penguins' diving depths and
times.
Calculate the F-statistic for the regression by filling in the
ANOVA table.
SS
df
MS
F-statistic
Regression
Residual
1628.4056
Total
367385.9237
CHAPTER 7: REGRESSION/PREDICITION
Key Terms
----------------------------------------------------------------------------------------------------------------------------
Least squares prediction equation --- The equation that
minimizes the total of all squared prediction errors for known Y
scores in the original correlation analysis.
Standard error of prediction --- A rough measure of the
average amount of predictive error
Squared correlation coefficient --- The proportion of
the total variance in one variable that is predictable from its
relationship with the other variable
Variance interpretation of r²---The proportion of
variance explained by, or predictable...
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?
Q1. Write down the equation of the regression straight line (the least-squares line)
Q2. For an increase of 1 mg of fertiliser applied, what is the average change in the wet weight of maize plants?
Q3. How are the two variables associated with each other? (Answer in 1 or 2 sentences)Q4. Determine the average weight of plants grown with 100mg of fertiliser applied. (round up your answer to 2 decimal places)Q5. Determine the average weight of plants grown with...