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)

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Chapter1: Equations And Graphs
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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.
Transcribed Image Text: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.
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