Multiple Regression Analysis For the attached data, find the multiple linear regression formula using X1 as the dependent variable and X2-X7 as the indepen

Multiple Regression Analysis For the attached data, find the multiple linear regression formula using X1 as the dependent variable and X2-X7 as the indepen

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  1. For the attached data, find the multiple linear regression formula using X1 as the dependent variable and X2-X7 as the independent variables.
  2. Using whatever means necessary find the model of best fit and justify your choices.
  3. Determine what variables are significant at a sig. level of 10%.  
  4. State what independent variable if any should be tested for interaction.
  5. Choose any two observed variables and calculate their residuals.
  6. What are the 4 assumptions about the error terms, (residuals) that need to be in order to perform multiple linear regression.

64 Finance & economics The Economist July 25th 2020

The global downturn of 2020 is probably the most quantifiedon record. Economists, firms and statisticians seeking to gauge
the depth of the collapse in economic activity and the pace of the
recovery have seized upon a new dashboard of previously obscure
indicators. Investors eagerly await the release of mobility statis-
tics from tech companies such as Apple or Google, or restaurant-
booking data from OpenTable, in a manner once reserved for offi-
cial inflation and unemployment estimates. Central bankers pep-
per their speeches with novel barometers of consumer spending.
Investment-bank analysts and journalists tout hot new measures
of economic activity in the way that hipsters discuss the latest
bands. Those who prefer to wait for official measures are regarded
as being like fans of u2, a sanctimonious Irish rock group: stuck
behind the curve as the rest of the world has moved on.

The main attraction of real-time data to policymakers and in-
vestors alike is timeliness. Whereas official, so-called hard data,
such as inflation, employment or output measures, tend to be re-
leased with a lag of several weeks, or even months, real-time data,
as the name suggests, can offer a window on today’s economic
conditions. The depth of the downturns induced by covid-19 has
put a premium on swift intelligence. The case for hard data has al-
ways been their quality, but this has suffered greatly during the
pandemic. Compilers of official labour-market figures have strug-
gled to account for furlough schemes and the like, and have plas-
tered their releases with warnings about unusually high levels of
uncertainty. Filling in statisticians’ forms has probably fallen to
the bottom of firms’ to-do lists, reducing the accuracy of official
output measures.

In some countries with dodgy official statistics, economists
have no choice but to rely on alternative indicators (see Middle
East & Africa section). In the rich world, though, official figures are
still the benchmark for high-quality economic information. The
methodologies used to construct them are, in the main, transpar-
ent and they have track records dating back decades, over the
course of several economic cycles. The same cannot be said about
many of the indicators that are currently in vogue.

Take, for example, the mobility data from Apple and Google
that have drawn so much attention in financial markets. The tech

firms should be commended for making the figures available so
quickly, and at a level of granularity that allows for a detailed look
at travel patterns. But the numbers need to be treated as what they
are—a measure of mobility—and not a proxy for overall economic
activity. They may reveal that more people are returning to work-
places, but not whether they were previously working from home
or out of the labour force altogether. Nor can they show whether
commuters are spending more or less on their coffees and sand-
wiches. Both Apple and Google present their figures relative to a
pre-pandemic benchmark of travel in January. That made sense in
February and March. Now, however, it could mislead. The latest
mobility reports show that visits to non-food retail stores in some
European countries are above those in January. But spending hab-
its often have a seasonal pattern, which needs to be taken into ac-
count. Oxford Economics, a consultancy, cautions that consumer
spending in Europe is usually 5-15% higher in July than in January.

You might think that figures on debit- and credit-card transac-
tions provide a better estimate of household spending. In June
Andy Haldane, the Bank of England’s chief economist, pointed to a
bounce-back in one such measure as evidence that Britain’s recov-
ery from the depths of lockdown was “so far, so v”. But even here
the signal is blurred. With many businesses keen to avoid cash
transactions to prevent the spread of infection, card spending may
be inflated by a substitution away from physical money. Even in
countries where contactless payment is common, cash was still
more likely to be used in small-value transactions before the pan-
demic. Adjusting for this shift is especially tricky.

Real-time indicators with a narrower focus, such as measures
of seated diners in restaurants or job vacancies posted on recruit-
ment websites, probably provide an accurate gauge of activity in
smaller pockets of the economy. But these are of limited use to
policymakers trying to see the big picture. Part of the problem is
that, as most of the data are collected by smartphones and con-
sumer-facing websites, most real-time measures shine a light on
consumers’ spending. But, though household spending is the sin-
gle largest component of gdp, it is the smaller, more volatile com-
ponents that tend to drive the business cycle. Companies’ capital
spending is trickier to measure in real time than restaurant vis-
its—but much more important to overall economic performance.

No better than the real thing
The value of real-time measures will be tested once the swings in
economic activity approach a more normal magnitude. Mobility
figures for March and April did predict the scale of the collapse in
gdp, but that could have been estimated just as easily by stepping
outside and looking around (at least in the places where that sort of
thing was allowed during lockdown). Forecasters in rich countries
are more used to quibbling over whether economies will grow at
an annual rate of 2% or 3% than whether output will shrink by 20%
or 30% in a quarter. Real-time measures have disappointed before.
Immediately after Britain’s vote to leave the European Union in
2016, for instance, the indicators then watched by economists
pointed to a sharp slowdown. It never came.

Real-time data, when used with care, have been a helpful sup-
plement to official measures so far this year. With any luck the best
of the new indicators will help official statisticians improve the
quality and timeliness of their own figures. But, much like u2, the
official measures have been around for a long time thanks to their
tried and tested formula—and they are likely to stick around for a
long time to come. 7

Real-time dangerFree exchange

Why novel and timely measures of economic activity should be treated with caution

Reproduced with permission of copyright owner. Further reproduction
prohibited without permission.

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