Use the dataset that you have been using for the previous projects.
Use all of your independent variables, your response variable, and the lm() function to build a multiple linear regression model.
Print the model with the summary() function. The output will be similar to the bottom of page 141.
Use the pairs() function to look at the scatterplots of the interval/ratio variables. Color your points by the value of a nominal/ordinal variable.
A standard regression model with correlated independent variables will almost always perform poorly. For this project, you will remove independent variables until the model is trustworthy.
Use the summary() output, and the scatterplots to decide if a variable should be removed. Remove the variable.
Repeat the process of
• build model
• check summary() and scatterplots
• remove variable
until you believe all variables in the model should stay in the model.
Use par(mfrow = c(2,2)) and the plot() function to look at diagnostic plots of the reduced model (similar to the plots on page 129).
Grading criteria:
• full model
• summary()
• pairs()
• remove independent variables, print reduced model each time (60% of grade)
• plot() final model
Create a simple linear regression model with one of your numeric independent variable and your response variable.
Build the scatterplot of the response variable by the independent variable, and the scatterplot of the residuals by the independent variable (similar to figure 3.3, page 50). Include the line of best fit on the first scatterplot. Also, plot the residuals by the response variable. Do you the scatterplots indicate that there are any problems with the model?
Use hist() to plot a histogram of the residuals. Do the residuals appear to be normally distributed?
Use qqnorm() and qqline() to plot a QQ-normal plot with the QQ-line of the residuals. Do the residuals appear to be normally distributed?
Use par(mfrow = c(2,2)) and plot(‘linear model’) to build a plot similar to figure 3.14 on page 70.
Record which data points are labeled in the subplots, then print those observations. Investigate each of these points and decide which ones are legitimate data points and which ones are erroneous and polluting your dataset.
Use car::powerTransform() to find power transformations for
• y – min(y) + 1, and
• x – min(x) + 1.
Transform the data and call the new data y_new and x_new. Build four scatterplots.
• y ~ x
• y_new ~ x
• y ~ x_new
• y_new ~ x_new
Which of these models appears to be the be fit? Build the corresponding linear model.
Grading Criteria:
• Simple linear regression model (no transformations)
• Scatterplot y ~ x
• Scatterplot residuals ~ x
• Scatterplot residuals ~ y
• hist(residuals)
• QQ-norm plot
• Linear model four plots
• Leverage data
• Four post-transformation scatterplots
• New linear model

Sample Solution

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TR Ltd. is a Canadian-controlled private corporation operating a franchised retail and mail-order
business in Toronto, Ontario. You may use whatever address and postal code you wish. The
business number for TR is 11111-1118 RC0001. Denver Chan, the company’s president, owns
100% of the corporation’s share capital. For the year ended November 30, 2020 (first full year of
operation), TR Ltd.’s financial statement reported income of $157,090 (see exhibit I for detailed
financial statements).
You have been retained to help prepare the company’s first tax return and to advise on other taxrelated matters. Financial information relating to the 2020 taxation year and to the corporation’s
financial statement is summarized below.
TR Ltd. – Selected Financial Information

1. The following properties were purchased for the new business:
   Franchise $ 40,000
   Land 30,000
   Building 270,000
   Delivery truck 40,000
   The franchise, purchased on December 1, 2019, permits the corporation to operate under
   the TR name for a period of 15 years. A renewable period of another 15 years is available,
   subject to satisfactory performance. The land cost of $30,000 consists of the purchase price
   of $20,000, $7,000 for permanent landscaping, and $3,000 for water and sewer
   connections. The building was constructed after March 18, 2007. On October, 15, 2020, the
   truck was involved in an accident. The damage was not repairable, and TR immediately
   signed an agreement with the insurance company to settle the claim for $31,000. The cash
   was received on December 10, 2020. Another truck was obtained under a lease
   arrangement. Amortization expense of $28,000 has been deducted from income.
2. Legal expense includes the following costs:
   Preparing annual corporate minutes $ 300
   Incorporation costs for TR Ltd. 1,500
   Negotiation of franchise agreement 2,000
3. Repairs and maintenance expense includes the following items:
   Paving the parking lot $8,000
   Cleaning and supplies 1,400
   Replacing a broken window 1,000
   Small tools costing less than $500 1,200
4. Advertising expense includes a cost of $7,000 to acquire a permanent mailing list for the
   mail-order business. The list has an expected life of six years. Other advertising items are
   listed below:
   Cost of making a television commercial $25,000
   Travel costs for Denver to attend a franchiser convention. Denver’s
   spouse travelled with him and attended a social function
   (souse’s expenses were $1,500) 3,000
   Charitable donations 2,000
   Meals and beverage costs for entertaining suppliers 1,800
   Costs of leasing and maintaining a pleasure boat to entertain
   suppliers and employees 2,600
   Television advertising
   Toronto station 11,000
   Buffalo USA station directed at the Toronto Canada market 6,000
5. A contingent reserve for possible defective products of $5,000 was recorded as a charge
   against cost of sales. During the year, $3,000 of products were returned.
6. On May 31, 2020, TR invested $40,000 in a one-year bank certificate earning annual
   interest of 7%. TR intends to recognize the interest revenue upon receipt at its one-year
   anniversary date.
7. Interest expense includes $14,000 on the building mortgage and $700 from a temporary
   bank loan of $12,000. The bank loan funds were, in turn, loaned, without interest, to Y
   Ltd., a corporation owned by Denver’s brother. Y Ltd. used all of its assets to operate an
   active business but declared bankruptcy in November 2020.
8. TR is planning to sell a new product in 2021—a bracelet with a charm depicting a popular
   cartoon character. The bracelet and charm will be ordered from separate suppliers, and
   TR’s staff will assemble the two pieces and package them in a specially designed box.
9. Shortly after incorporation, TR acquired 46% of the voting common shares of Q Ltd., a
   Canadian-controlled private corporation that supplies certain products to TR and other
   retailers. On October 31, 2020, TR received a non-eligible dividend of $15,000 from Q Ltd.
   At the time, Q Ltd. had non-eligible RDTOH of $2,000. An opportunity exists for TR to
   purchase an additional 5% of the voting common shares of Q Ltd. early in 2021. A
   decision will be made in January 2021.
10. On November 30, 2020, TR declared and paid a non-eligible dividend of $40,000.
    EXHIBIT 1:
    Statement of Income
    Sales $1,474,590
    Cost of sales 810,000
    Gross profits 664,590
    Expenses:
    Salaries and wages $232,000
    Management bonuses 50,000
    Employee benefits 33,000
    Interest expenses 14,700
    Insurance 7,000
    Defective Products reserve 5,000
    Legal and accounting 3,800
    Repairs and maintenance 11,600
    Travel 8,000
    Advertising and promotion 58,400
    Bad debts 36,000
    Provision for sales returns 5,000
    Depreciation/amortization 28,000
    Donations 4,000
    Loss on sale of marketable securities 6,000 502,500
    162,090
    Other:
    Dividends received 15,000 15,000
    Net income before Income Taxes
    Income tax provision
    Net Income after Income taxes
    $ 177,090
    20,000
    157,090
    Opening Retained Earnings
    Less: Dividends Declared and Paid
    Ending Retained Earnings
    0
    40,000
    $117,090
    Balance Sheet
    ASSETS:
    Current Assets:
    Cash $2,000
    Accounts Receivable
    Loan Receivable
    Bank Certificate
    Inventory
    130,000
    12,000
    40,000
    80,000
    Prepaid Expenses 4,590
    Total Current Assets 268,590
    Property, Plant and Equipment
    Delivery Truck
    Franchise
    $0
    40,000
    Land 30,000
    Building 270,000
    340,000
    Less Accumulated Amortization 28,000
    Total Property, Plant and Equipment
    Investment in Q Ltd.
    312,000 312,000
    58,000
    Total Assets $638,590
    LIABILITIES:
    Accounts Payable and accrued liabilities
    Loan Payable
    $214,500
    12,000
    Taxes Payable 20,000
    Due to shareholders 136,000
    Total Liabilities 382,500
    SHAREHOLDERS’ EQUITY
    Share Capital 139,000
    Retained Earnings 117,090
    Total Shareholders’ Equity $ 256,090
    Total Liabilities and Shareholders’ Equity $638,590

Sample Solution

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