Statistics

Ridge regression is used in linear regression to deal with multicollinearity. It reduces the MSE of the model in exchange for introducing some bias.

A decimal becase a decimal can be any fraction

Any integer from 3 to 18

171.6

The Kolmogorov-Smirnov one sample test.

If repetitions of digits is not allowed, then 5! (which is 5-factorial = 5*4*3*2*1). If you assume repetition of digits is allowed, then 55.

More detail:

The math category this falls under is called combinatorix - counting the number of ways to combine things. The first answer, 5!, comes from the following reasoning:

There are 5 possibilities for the first place. Once you have chosen that places, there are four choices remaining for the next digit for each of those choices, thus giving you 5*4, and thus logic continues for the remaining digits.

For the other answer, the logic is the same, but since there is repetition allowed, each places has 5 choices.

3. It occurs six times, whereas 5 only occurs twice, and the rest that occur, occur once.

yes

There is not enough information to answer the question sensibly. Is it implied that out of 200 students not one knew the answer to any one of the seven questions? And that all pupils had to make random choices for each question? Is that at all credible?

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to control the pointer

no the y

47, 94, 141, 188, 235

1/8 or 12.5%

Yes, if 0 is a valid response.

It is 1/36.

8:19

A z-test is a statistical test which compares a test statistic - the z-score - which is based on data with the standard normal distribution. If used appropriately (very often it isn't) it will indicate the probability, under a null hypothesis, of observing an outcome at least as extreme.

A simple z is a letter of the alphabet. In algebra it is used to denote variables; in coordinate geometry it is usually used to denote the third orthogonal direction for the coordinate space.

The median is the value that is in 'the middle'. That is, half the values fall below it, half above it. There are a total of 3 + 5 + 6 = 14 sample values. There is no 'middle' value exactly since there are an even number of values.

Both the 7th and the 8th largest value are 100 g. Their average is 100 g. Therefore, the median of this sample is 100 g.

1/6 = 16 2/3 percent

99997

Yes.

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Standardising the observation ensures that the mean is 0 and the standard error is 1. Otherwise the plot could be located anywhere and be concentrated or spread out.