SHOW ALL THE WORK OR SEND LINK 1. The data below represent: Y, the assessed valu
ID: 3318893 • Letter: S
Question
SHOW ALL THE WORK OR SEND LINK
1. The data below represent: Y, the assessed value in thousands of dollars; X1, the size of the house in thousands of square feet; X2, whether or not the house has a swimming pool
Assessed Value Square Feet Swimming pool?
79.5 1.69 no
81.3 1.79 yes
71.5 1.31 yes
77.9 1.52 no
88.4 1.99 yes
72.7 1.62 no
85.6 1.92 yes
Give the equation of the regression line rounded to 3 decimal places.
Interpret the slope of square footage in the context of this problem. Decimal must be moved appropriately
Interpret the slope of swimming pool? in the context of this problem Decimal must be moved appropriately
Predict the assessed value of the house for a square footage of 1730 square feet and with a swimming pool Decimal must be moved appropriately
2. A sample of students was taken measuring the hours studied for a test and the score on the test (out of a possible total of 350 points)
X(# hours study) Y (Score on test)
5 155
7 210
8 150
10 192
11 245
13 260
15 270
18 275
20 290
a). Give the following:
i) sum of the x
ii) sum of the y
iii) sum of the x squared
iv) sum of the xy
v) sum of the y squared
b) Find b sub 0 and b sub 1 using the formulas in Excel that were used in the module. Round to 3 decimal places.
c) Find the equation of the regression line.
d) What is the value of the slope and interpret its meaning in the context of this problem
e) Predict the test score for 13 hours of study.
f) Calculate the coefficient of determination by writing the formula in Excel. Show your calculations.
g) What % of the variation in test scores is explained by the # hours of study?
h) What % is due to other factors?
i) Name 1 other factor that could affect a test score.
j) What is the calculated F in testing the null hyothesis: no significant relation between # hours of study and test scores. (You must use the Tool-Pak for this.)
k) What is the p-value?
l) Is there a significant relation between #hours of study and test scores? Please answer yes or no.
3. The following data give the sales in millions of dollars for a company for the given years:
Years Sales
2001 3.1
2002 3.6
2003 4.3
2004 4.9
2005 5.2
2006 6.1
2007 6.9
2008 7.2
a) Give the equation of the trend line for this time series. Round to 3 decimal places.
b) Interpret the intercept in the context of this problem. Move decimal appropriately in your answer.
c) Interpret the slope of sales in the context of this problem. Move decimal appropriately in your answer.
d) Forecast sales for the year 2012. Move decimal appropriately in your answer.
e) What % of the increase in sales is explained by the lineaer trend over the time series?
4. The data below represent Y, sales in thousands of dollars; X1, price in cents; X2, promotion in dollars.
Sales Price Promotion
53 674 3250
59 628 3589
61 536 4266
63 521 4875
65 528 4912
71 506 5763
76 453 6173
83 399 6369
a) Give the equation of the regression line. Round to 3 decimal places.
b) Give the value of the slope for price
c) Interpret its meaning in the context of this problem. Move ethe decimal appropriately
d) Give the value of the slope for promotion.
e) Interpret its meaning in the context of this problem. Move the decimal appropriately.
f) Predict sales for price of $4.50 and $6000 spent on promotion. Move the decimal appropriately.
g) Give the calculated F for testing if the relationship is significant between sales & price and promition.
h) What is its p-value?
i) Is the relationship significant? Please answer yes or no.
j) Give the coefficient of determination.
k) Interpret its meaning in the context of this problem.
l) Give the coefficient of partial determination for price. Show your calculations.
m) Interpret its meaning in the context of this problem.
n) Give the coefficient of partial determination for promotion. Show your calculations.
o) Interpret its meaning in the context of this problem.
5. Your factory produces 5 styles of coats. There are 5 rectangular areas (length and width in ft. are given) for each style of coat. Workers are paid $25 per hour. From the data below, find for each style:
1) the total wholesale $, 2) the total wages paid, 3) the total production cost, 4) the costs + wages as % of wholesale $. Remember wholesale $ is only for acceptable coats as we don't sell rejects. Production costs are in dollars.
Style of coat: length of area width of area #acceptable #rejected prod. cost$ each coat/sq. ft. wholesale$/coat # worker hrs/coat
1 135 95 5786 452 .02 435 3.5
2 120 105 4468 354 .04 347 4.1
3 140 120 5637 259 .03 320 3.9
4 130 80 4903 395 .01 310 3.1
5 125 90 4039 349 .02 298 2.9
Explanation / Answer
R code:
> y=c(79.5,81.3,71.5,77.9,88.4,72.7,85.6) # assessed value
> x1=c(1.69,1.79,1.31,1.52,1.99,1.62,1.92) #size of house
> x2=c(0,1,1,0,1,0,1) #swimming pool present : 1, not present : 0
> x2=as.factor(x2) # factorization
> model=lm(y~x1+x2) #fitting linear model
> summary(model)
Call:
lm(formula = y ~ x1 + x2)
Residuals:
1 2 3 4 5 6 7
0.95874 -1.26309 -0.01552 3.27142 1.23375 -4.23016 0.04486
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 39.645 8.608 4.605 0.00999 **
x1 23.016 5.248 4.386 0.01182 *
x21 1.720 2.306 0.746 0.49716
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 2.856 on 4 degrees of freedom
Multiple R-squared: 0.8596, Adjusted R-squared: 0.7894
F-statistic: 12.24 on 2 and 4 DF, p-value: 0.01971
The regression equation : Assessed value = 39.645 + 23.016*Size + 1.72*Swimming pool present or not
The slope intercept of size = 23.016 means that the assessed value will increase by 23.016 thousands $ when there is an increase of 1 square foot in the size of the house.
The slope intercept of the swimming pool = 1.72 means that the assessed value will increase by 1.72 thousands $ when there is a swimming pool present in the house.
Assessed value = 39.645 + 23.016*1730/1000 + 1.72*1 = $ 81.183 thousands.
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