The following output from R presents the results from computing a linear model. In our data example we are interested to study the relationship between TV budget and sales This R output is for a simple data set that contains, in thousands of dollars, TV budget for 200 different markets along with the Sales, in thousands of units, for each market. summary (model1)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![The following output from R presents the results from computing a linear model.
In our data example we are interested to study the relationship between TV budget and sales This R output
is for a simple data set that contains, in thousands of dollars, TV budget for 200 different markets along
with the Sales, in thousands of units, for each market.
summary (model1)
##
## Call:
## Lm (formula = Sales
TV, data = train)
##
## Residuals:
##
Min
10 Median
30
Max
## -8.5816 -1.7845 -0.2533
2.1715
6.9345
##
## Coefficients:
##
Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.764098
## TV
0.607592
11.13
<2e-16 ***k
0.050284
0.003463
14.52
<2e-16 ***
##
---
O '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Signif. codes:
#2#
## Residual standard error: 3.204 on 120 degrees of freedom
## Multiple R-squared: 0.6373, Adjusted R-squared: 0.6342
## F-statistic: 210.8 on 1 and 120 DF, p-value: < 2.2e-16
confint (model1)
##
2.5 %
97.5 %
## (Intercept) 5.56110868 7.96708701
## TV
0.04342678 0.05714057
a. Find the least squares regression line by choosing appropriate dependent and independent variables
based on your answer in part a.
b. Interpret the meaning of the values of band bị calculated in part b.
c. Calculate r and r?, and explain what they mean.
d. Compute the standard deviation of errors.
e. Construct a 95% confidence interval for slope B1.
f. Using alpha=0.05, test whether B, is different from zero
g. Test at a 5% significance level whether B, is negative.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fad962c-823b-45ab-b4bd-c6bef8709229%2Fbeb7a994-9b09-4caa-941e-978b280dd882%2Ftm4eypv_processed.png&w=3840&q=75)
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