Q4). The following are advertised sale prices of color televisions at an electro
ID: 3376541 • Letter: Q
Question
Q4). The following are advertised sale prices of color televisions at an electronics store.
Part (a) Decide which variable should be the independent variable and which should be the dependent variable.
Independent variable: size; Dependent variable: sale price
Independent variable: sale price; Dependent variable: size
Part (b) Make a scatter plot of the data.
Part (c) Does it appear from inspection that there is a relationship between the variables? Why or why not?
Yes, it appears that the television cost increases with television size.
No, there is no visible relationship between the variables.
Part (d) Calculate the least squares line. Put the equation in the form of: ? = a + bx. (Round your answers to three decimal places.)
? = + x
Part (e) Find the correlation coefficient r. (Round your answer to four decimal places.)
r = ( )
Is it significant?
Yes
No
Part (f) Find the estimated sale price for a 34-inch television. (Use your equation from part (d). Round your answer to two decimal places.)
$
Find the estimated sale price for a 51-inch television. (Use your equation from part (d). Round your answer to two decimal places.)
$
Part (g) Use the two points in part (f) to plot the least squares line.
Part (h)
Does it appear that a line is the best way to fit the data? Why or why not?
A line does appear to be the best way to fit the data because the data follow a weak positive trend.
A line is the best way to fit the data because the slope of the line is positive and the linear correlation is positive.
A line does not appear to be the best way to fit the data because the data do not follow a linear trend.
A line does not appear to be the best way to fit the data because it does not touch all the data points.
Part (i) Are there any outliers in the above data?
Yes, (9, 157) is an outlier.
Yes, (40, 2177) is an outlier.
Yes, (60, 2497) is an outlier.
No, there are no outliers.
Part (j) What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.)
( )
Interpret the slope.
As sale price of the television increases by $1, the size decreases by this many inches.
As the size of the television increases by one inch, the sale price increases by this many dollars.
As sale price of the television increases by $1, the size increases by this many inches.
As the size of the television increases by one inch, the sale price decreases by this many dollars.
Size (inches) Sale Price ($) 9 157 20 197 27 267 31 447 35 1177 40 2177 60 2497 Sale Price 2500 2000 1500 1000 500F 10 20 30 40 50 L Size (in) 60Explanation / Answer
Result:
Part (a) Decide which variable should be the independent variable and which should be the dependent variable.
Answer: Independent variable: size; Dependent variable: sale price
Independent variable: sale price; Dependent variable: size
Part (b) Make a scatter plot of the data.
Top left Graph
Part (c) Does it appear from inspection that there is a relationship between the variables? Why or why not?
Answer: Yes, it appears that the television cost increases with television size.
No, there is no visible relationship between the variables.
Part (d) Calculate the least squares line. Put the equation in the form of: ? = a + bx. (Round your answers to three decimal places.)
? = -746.362+ 54.701 x
Part (e) Find the correlation coefficient r. (Round your answer to four decimal places.)
r = (0.8915 )
Is it significant?
Answer: Yes
No
Part (f) Find the estimated sale price for a 34-inch television. (Use your equation from part (d). Round your answer to two decimal places.)
Y = -746.3615+54.7006*34 =1113.4589
$ 1113.46
Find the estimated sale price for a 51-inch television. (Use your equation from part (d). Round your answer to two decimal places.)
Y = -746.3615+54.7006*51 =2043.3691
$2043.37
Part (g) Use the two points in part (f) to plot the least squares line.
Part (h)
Does it appear that a line is the best way to fit the data? Why or why not?
A line does appear to be the best way to fit the data because the data follow a weak positive trend.
A line is the best way to fit the data because the slope of the line is positive and the linear correlation is positive.
Answer: A line does not appear to be the best way to fit the data because the data do not follow a linear trend.
A line does not appear to be the best way to fit the data because it does not touch all the data points.
Part (i) Are there any outliers in the above data?
Yes, (9, 157) is an outlier.
Yes, (40, 2177) is an outlier.
Yes, (60, 2497) is an outlier.
No, there are no outliers.
Part (j) What is the slope of the least squares (best-fit) line? (Round your answer to three decimal places.)
(54.701 )
Interpret the slope.
As sale price of the television increases by $1, the size decreases by this many inches.
Answer: As the size of the television increases by one inch, the sale price increases by this many dollars.
As sale price of the television increases by $1, the size increases by this many inches.
As the size of the television increases by one inch, the sale price decreases by this many dollars.
Regression Analysis
r²
0.7949
n
7
r
0.8915
k
1
Std. Error
490.144
Dep. Var.
Sale Price ($)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
4,654,082.2977
1
4,654,082.2977
19.37
.0070
Residual
1,201,203.4166
5
240,240.6833
Total
5,855,285.7143
6
Regression output
confidence interval
variables
coefficients
std. error
t (df=5)
p-value
95% lower
95% upper
Intercept
-746.3615
435.5093
-1.714
.1472
-1,865.8738
373.1508
Size (inches)
54.7006
12.4279
4.401
.0070
22.7536
86.6476
Regression Analysis
r²
0.7949
n
7
r
0.8915
k
1
Std. Error
490.144
Dep. Var.
Sale Price ($)
ANOVA table
Source
SS
df
MS
F
p-value
Regression
4,654,082.2977
1
4,654,082.2977
19.37
.0070
Residual
1,201,203.4166
5
240,240.6833
Total
5,855,285.7143
6
Regression output
confidence interval
variables
coefficients
std. error
t (df=5)
p-value
95% lower
95% upper
Intercept
-746.3615
435.5093
-1.714
.1472
-1,865.8738
373.1508
Size (inches)
54.7006
12.4279
4.401
.0070
22.7536
86.6476
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