Business Statistics: A First Course (8th Edition)
8th Edition
ISBN: 9780135177785
Author: David M. Levine, Kathryn A. Szabat, David F. Stephan
Publisher: PEARSON
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A materials engineer working for a furniture manufacturer wants to evaluate the rigidity of the particle board used by the manufacturer. The engineer collects stiffness data from pieces of particle board that have different densities at different temperatures.
Determine the connection between the stiffness and the density of the wood.
What does Pierson's r tell us?
What is the regression between the stiffness and the density of the wood?
Write the equation of the linear regression?
density
rigidity
Temp
9.5
14.814
70.61056
8.4
17.502
73.34893
9.8
14.007
66.15377
11
19.443
70.05781
8.3
7.573
69.33919
9.9
14.191
69.12882
8.6
9.714
69.83351
6.4
8.076
64.36617
7
5.304
65.41039
8.2
10.728
67.76739
17.4
43.243
69.70053
15
25.319
66.93095
15.2
28.028
71.52362
16.4
41.792
66.60748
16.7
49.499
67.98685
15.4
25.312
64.29324
15
26.222
64.48343
14.5
22.148
71.3084
14.8
26.751
69.58755
13.6
18.036
71.13321
25.6
96.305
72.09707
24.4
72.594
67.32207…
Nassau County is located approximately 25 miles east of New York City. The accompanying data include the fair market value (in thousands of dollars), land area of the property in acres, and age, in years, for a sample of 20 single-family homes located in
Glen Cove, a small city in Nassau County. Develop a multiple linear regression model to predict the fair market value based on land area of the property and age, in years. Complete parts (a) through (f).
Click the icon to view the data table.
a. State the multiple regression equation. Let X1; represent the land area of the property in acres and let X2 represent age, in years.
Ý; = 458.4 + ( 421.7) ×1 + ( – 1.8) X21
-
(Round to one decimal place as needed.)
b. Interpret the meaning of the slopes, b, and b2, in this problem. Choose the correct answer below.
O A. For a given age, each increase of 1 acre in land area is estimated to result in an increase in fair market value by b, dollars. For a given land area, each increase in one year…
A b c
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- The model developed from sample data that has the form of Yhat = bo +bjX is known as the multiple regression model with two predictor variables. (True or False) O True O Falsearrow_forwardThe accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter a)The predicted y-hat value for a diameter of 201 is 864. Interpret this predicted value. b)what is the predicted strength of a weld with a diameter of 51?arrow_forwardIn a study of housing demand, the county assessor is interested in developing a regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor feels that the most important variable affecting selling price (measured in thousands of dollars) is the size of house (measured in hundreds of square feet). He randomly selected 15 houses and measured both the selling price and size, as shown in the following table. OBSERVATIONi SELLING PRICE (× $1,000)Y SIZE (× 100 ft2 )X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 265.2 279.6 311.2 328.0 352.0 281.2 288.4 292.8 356.0 263.2 272.4 291.2 299.6 307.6 320.4 12.0 20.2 27.0 30.0 30.0 21.4 21.6 25.2 37.2 14.4 15.0 22.4 23.9 26.6 30.7 a. Plot the data.b. Determine the estimated regression line. Give an economic interpretation of the estimated slope (b) coefficient.c. Determine if size is a statistically significant variable in estimating selling price.d. Calculate the coefficient…arrow_forward
- The trip rate (y) and the corresponding household sizes (x) from a sample are shown in Table Q2. Apply the regression method to find the trip rate for a household size of 10. Table Q2arrow_forwardThe data below is for a hypothetical study investigating the Systolic Blood Pressure (SBP) of construction workers. The table shows respective measurements of 20 workers along with hours of work per day and the area of the city the work took place. [You can use Excel-Data Analysis – Regression or http://vassarstats.net/multU.html] SBP Hrs/day Area 109.6 7 east 107.4 8 east 140.3 9 east 146.5 12 east 98.2 6 east 137.8 9 east 124.1 10 east 113.2 8 east 127.8 9 east 125.3 8 east 108.5 6 west 181.3 13 west 137.4 10 west 146.2 10 west 142.4 9 west 123.7 8 west 129.6 8 west 143.6 9 west 160.7 11 west 148.3 9 west a) What is the regression equation? b) Interpret the meaning of the slopes in this problem. d) At the 0.05 level of significance, determine whether each independent variable makes a contribution to the…arrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbados estimated the following multiple regression model using yearly data spanning the period 2001 to 2016: FR=a+BOIL+YEXP+8FDI Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports (S000's) and FDI = annual foreign direct investment (S000's). The sample of data was processed using MINITAB and the following is an extract of the output obtained: Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491 OIL 85.39 18.46 4.626 0.0006 EXP -377.08 112.19 0.0057 FDI -396.99 160.66 -2.471 ** s = 2.45 R-sq = 96.3% R-sq (adj) = 95.3% Analysis of Variance Source DF MS F Regression 3 1991.31 663.77 ? ?? Error 12 77.4 6.45 Total 15 a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ***, ***', ?'and ??' d) Hence test whether ß is significant. Give reasons for your answer. e) Perform…arrow_forward
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